Answers
1. As you can tell from the function definition and plot, there's a discontinuity at x = -2. But in the limit from either side of x = -2, f(x) is approaching the value at the empty circle:
[tex]\displaystyle \lim_{x\to-2}f(x) = \lim_{x\to-2}(x-2) = -2-2 = \boxed{-4}[/tex]
Basically, since x is approaching -2, we are talking about values of x such x ≠ 2. Then we can compute the limit by taking the expression from the definition of f(x) using that x ≠ 2.
2. f(x) is continuous at x = -1, so the limit can be computed directly again:
[tex]\displaystyle \lim_{x\to-1} f(x) = \lim_{x\to-1}(x-2) = -1-2=\boxed{-3}[/tex]
3. Using the same reasoning as in (1), the limit would be the value of f(x) at the empty circle in the graph. So
[tex]\displaystyle \lim_{x\to-2}f(x) = \boxed{-1}[/tex]
4. Your answer is correct; the limit doesn't exist because there is a jump discontinuity. f(x) approaches two different values depending on which direction x is approaching 2.
5. It's a bit difficult to see, but it looks like x is approaching 2 from above/from the right, in which case
[tex]\displaystyle \lim_{x\to2^+}f(x) = \boxed{0}[/tex]
When x approaches 2 from above, we assume x > 2. And according to the plot, we have f(x) = 0 whenever x > 2.
6. It should be rather clear from the plot that
[tex]\displaystyle \lim_{x\to0}f(x) = \lim_{x\to0}(\sin(x)+3) = \sin(0) + 3 = \boxed{3}[/tex]
because sin(x) + 3 is continuous at x = 0. On the other hand, the limit at infinity doesn't exist because sin(x) oscillates between -1 and 1 forever, never landing on a single finite value.
For 7-8, divide through each term by the largest power of x in the expression:
7. Divide through by x². Every remaining rational term will converge to 0.
[tex]\displaystyle \lim_{x\to\infty}\frac{x^2+x-12}{2x^2-5x-3} = \lim_{x\to\infty}\frac{1+\frac1x-\frac{12}{x^2}}{2-\frac5x-\frac3{x^2}}=\boxed{\frac12}[/tex]
8. Divide through by x² again:
[tex]\displaystyle \lim_{x\to-\infty}\frac{x+3}{x^2+x-12} = \lim_{x\to-\infty}\frac{\frac1x+\frac3{x^2}}{1+\frac1x-\frac{12}{x^2}} = \frac01 = \boxed{0}[/tex]
9. Factorize the numerator and denominator. Then bearing in mind that "x is approaching 6" means x ≠ 6, we can cancel a factor of x - 6:
[tex]\displaystyle \lim_{x\to6}\frac{2x^2-12x}{x^2-4x-12}=\lim_{x\to6}\frac{2x(x-6)}{(x+2)(x-6)} = \lim_{x\to6}\frac{2x}{x+2} = \frac{2\times6}{6+2}=\boxed{\frac32}[/tex]
10. Factorize the numerator and simplify:
[tex]\dfrac{-2x^2+2}{x+1} = -2 \times \dfrac{x^2-1}{x+1} = -2 \times \dfrac{(x+1)(x-1)}{x+1} = -2(x-1) = -2x+2[/tex]
where the last equality holds because x is approaching +∞, so we can assume x ≠ -1. Then the limit is
[tex]\displaystyle \lim_{x\to\infty} \frac{-2x^2+2}{x+1} = \lim_{x\to\infty} (-2x+2) = \boxed{-\infty}[/tex]
Related Questions
Given the line 2x - 3y - 5 = 0, find the slope of a line that is perpendicular to this line.
Answers
Answer:
The slope of the line would be -3/2.
Step-by-step explanation:
Let's get this equation into the proper slope form:
2x - 3y - 5 = 0
2x - 3y + 3y - 5 = 0 + 3y
2x - 5 = 3y
(1/3)(2x - 5) = 3y * 1/3
2/3x - 5/3 = y
Since the slope is 2/3, we need to find the negative reciprocal of that number, which is -3/2.
First of all, we need to add 5 on both sides :
2x-3y=5
Now, subtract 2x on both sides ↓
-3y=5-2x
Or
-3y=-2x+5
Now we need to divide by -3 on both sides to get y all by itself ↓
y=-2/-3+5/-3
[tex]\boxed{\\\begin{minipage}{2cm}y=$\displaystyle\frac{2}{3} x-\frac{5}{3}$ \\ \end{minipage}}[/tex]
Now determining the slope is facile.
If lines are perpendicular to each other, they
Intersect at a 90º angleHave slopes that are opposite reciprocalsIn order to find the opposite reciprocal of a fraction, we need to switch the numerator & the denominator places and then change the fraction's sign as follows ↓
(slope = 2/3)
Switch the numerator and denominator places ↓
3/2
Change the fraction's sign ↓
-3/2
Therefore the slope's -3/2hope helpful ~
find the simple interest due on a 270-day loan of $20,000 at an interest rate of 8.875%
Answers
Answer:
first you need to take way 20,000-88.75 =19,911.25 now you need to multiple 19,911.25×270=3,982345.go and see for your self
HELE ME PLEASE!
Find the exact volume of the cylinder.
A)
4577 cm3
B)
90 cm3
C)
2257 cm3
D)
9001 cm3
Answers
Answer:
none of them are right not sure what's up with that.
Step-by-step explanation:
cylinder is base*height
base is pi*r^2, or 25pi
height is 9, so the volume is 225pi is about 707, so none of the answers are correct
please. im begging can you help me on this ?
Answers
Answer:
I think its B (x-5=13)
Step-by-step explanation:
if its x-5=13
Pedro bought 13 and 5
so 13+5 = 18 (x)
so rearrange the equation to be x-5=13
so imagine x=18 and it would work:
18-5=13
Answer: B. x - 5 = 13
Step-by-step explanation:
Since Pedro bought the picture frames for his mother, we will see what she does with them. 5 go to her sister and 13 are kept for herself. Let x be the number of picture frames Pedro buys.
5 + 13 = x
This is not one of the answer choice, but x - 5 = 13 is. If we subtract 5 from both sides of the equation we created above, this proves to be our answer.
B. x - 5 = 13
Marina bought a bag of 10 chocolate cookies, 35 vanilla cookies, and 30 peanut butter cookies.
If she selects a cookie from the bag without looking, what is the probability she selects a peanut butter cookie?
Answers
Answer:
[tex]\frac{2}{5}[/tex]
Step-by-step explanation:
1) Add all the values.
= 10 + 35 + 30
= 75
2) 75 will be the denominator and the one required will be the numerator.
Since there are 30 peanut butter cookies, the probability is [tex]\frac{30}{75}[/tex].
3) Simplify the fraction if necessary.
Divide both sides by 15.
= [tex]\frac{2}{5}[/tex]
Can some one help me with this ASAP
Answers
4x - 2y = 12
x + 2y = 8
(to cancel 2y, solve by adding)
4x - 2y = 12
+
x + 2y = 8
4x + x = 5x
-2y + 2y = 0
12 + 8 = 20
5x = 20
÷5
x = 4
Substitute x=4 to one of the equation:
x + 2y = 8
4 + 2y =8
-4
2y. = 4
÷2
y. = 2
Check:
4 + (2x2) does give you 8
Hope this helps!
2. Choose the graph that shows the solution of the inequality on the number line
c<-1
|||||||||
-6 -4 -2 0 2
|||||||→
-6
-4 -2 0 2
|||→
-6 -4 -2 0 2
++
6
-4 -20
Answers
Answer:
Number line 3 also known as [C]
Step-by-step explanation:
Given that:
c ≤ -1
Knowing that:
≤ = Less than or equal to
Now substitute into the equation:
C less than or equal to -1
Thus, it going left on a number line.
The only number line with left is [A] and [C]
Since ≤ = Less than or equal to -1
then, it including -1
also known as a closed circle means the number is included and an open circle means it is not.
Hence, it closed circle.
Thus, the answer is [C]
Kavinsky
find the volume of number ten pls i know the answer is 449.57 the figure is to the left
Answers
Answer:
see below ( I do not think 449.57 m^2 is correct for surface area)
Surface area = 374.65 m^2 Volume = 448.83 = ~~ 449 m^3
Step-by-step explanation:
Find the SURFACE AREA (NOT the volume)
Height of cone = sqrt ( 13^2 - 4.5^2) = 12.1963 m
surface area equation for cone = pi * r * (r+ sqrt (h^2+r^2) ) = 247.4 m^2
Sphere surface area = 4 pi r^2 = 254.5 m^2
HEMIsphere is 1/2 of this = 127.235 m^2
Add the two surface areas = 374.65 m^2
For VOLUME: cone 1/3 pi r^2 h = 257.979 m^3
HEMIsphere = 1/2 4/3 pi r^3 = 190.851 m^3
Total VOLUME is then 448.83 m^3
Find the area of the perimeter and the area of the following figure.
Answers
Perimeter = (2+11+7+5+9+16)=50
area= 67cm squared
4.
Which statement best describes the figure shown below?
A The ray appears to be perpendicular to 2 line segments that appear to be
parallel
B The ray appears to be parallel to 2 line segments that appear to be
perpendicular.
C The line segment appears to be perpendicular to 2 lines that appear to be
parallel
D The line segment appears to be parallel to 2 lines that appear to be
perpendicular.
Answers
999999999999999999999999
PLEASE HELP!! I DON'T UNDERSTAND IT
Answers
5 - x divided by 3/4 x = 1/3
Answers
Answer:
x = 4
Step-by-step explanation:
(5-x) / (3/4x) = 1/3
multiply both sides by 3/4 x
5-x = 3/12 x add 'x' to both sides of the equation
5 = 15/12 x multiply both sides by 12/15
4 = x
-10x19=2x2 please do explanation
Answers
Answer:
x=0 or x=−95
Step-by-step explanation:
Step 1: Simplify both sides of the equation.
−190x=2x²
Step 2: Subtract 2x² from both sides.
−190x−2x²=2x²−2x²
−2x²−190x=0
Step 3: Factor left side of equation.
(−2x)(x+95)=0
Step 4: Set factors equal to 0.
−2x=0 or x+95=0
x=0 or x=−95
[tex]~~~~2x^2 =-10 \times 19\\\\\implies 2x^2 = -190\\\\\implies x^2 = -\dfrac{190}2\\\\\implies x^2 = -95\\\\\implies x = \pm\sqrt{-95}\\\\\implies x = \pm \sqrt{-1}\sqrt{95}\\\\\implies x = \pm i\sqrt{95}[/tex]
From a hot-air balloon, Enola measures a 22 degrees angle of depression to a landmark that’s 310 feet away, measuring horizontally. What’s the balloon’s vertical distance above the ground? Round your answer to the nearest hundredth of a foot if necessary.
Answers
Answer:
125.25 ft
Step-by-step explanation:
The geometry of the problem can be modeled by a right trianlge in which the side adjacent to the angle is 310 ft, and the side opposite the angle is the one we want to find. The relevant trig relation is ...
Tan = Opposite/Adjacent
__
Solving for the Opposite side (the height of the balloon), we find ...
Opposite = Adjacent · Tan
height = (310 ft)·tan(22°) ≈ 125.25 ft
Enola's balloon is about 125.25 ft above the ground.
_____
Additional comment
If we assume Enola's angle measurement can have a possible error of ±0.5°, then the corresponding error in the balloon height is more than ±3 ft. It is a bit of nonsense to report the height to the nearest 0.12 inches, (0.01 ft).
Find the equation of the parabola with a focus F (0, 3) and a directrix of y = -5.
Answers
Answer:
y=116⋅x2−1
Step-by-step explanation:
6] divide -7 by -4/5
whats the answer
Answers
[tex] - 7 \div \frac{ - 4}{5} [/tex]
solution:[tex] \frac{ - 7}{1} \div \frac{ - 4}{5} [/tex]
[tex] =8.75[/tex]
( just keep the first fraction as it is, change the divide sign to a multiply and flip the second fraction upside down. )
Answer:
35/4 or 8 3/4.
Step-by-step explanation:
-7 / -4/5
Invert the second fraction and multiply:
= -7 * -5/4
= 35/4
= 8 3/4.
How to figure out how to do this problem
Answers
How do my child do this
Answers
Matt bought 6 pie molds at a cost of $1.22 per mold. He also bought 6 pre-
made crusts at a cost of $0.97 per crust. How much did Matt spend on pie
molds?
Answers
Answer:
$13.14
Step-by-step explanation:
Find the circumference of a circle with diameter,
d
= 11.8cm.
Give your answer rounded to 3 SF.
Answers
Answer:6.8
Step-by-step explanation:
i dont know how to explain.
Got stuck, need help for solving the measure of arc LP.
Answers
Answer:
-3 degrees
Step-by-step explanation:
13x + 78= 39 degree
-78 -78
(divide both sides by 13)
Suppose you want to accumulate $120,000 for your retirement in 30 years.
Consider these two plans:
Plan A: make a single deposit into an account with an annual compounding and an APR of 5%.
Plan B: Make a single deposit into an account with continuous compounding and an APR of 4.8% 
1.) how much do you need to deposit in each amount in order to reach the goal?
2.) calculate the current APR the compounding period, and the claimed APY for your personal savings account. (Or pick a rate from a nearby bank)
3.) calculate the APY on your account (or someone u know)
4.) Does your calculation agree with the APY claimed by the bank?
Answers
The amount that would be needed to be deposited in order to reach the goal is:
Plan A: $27,765.29.Plan B: $28,431.33Calculations and Parameters:Since Plan A compounds annually at an apr of 5%.
and plan B compounds continuously at an apr of 4.8%
PART AUsing the formula for annual compounding
[tex]f = p * (1+r)^n[/tex]
Where
f is the future value which is equal to 120,000p is the present value.r is the interest rate per time period.n is the number of time periods.Because the compounding is done annually, then the APR/100= 0.05
Also, because the time periods are annual, hence, the time periods would be equal to the number of years = 30.
Putting the values together:
120,000 = p * (1.05)^30.
divide both sides of this formula [tex](1.05)^3^0[/tex] to get:
[tex]120,000 / (1.05)^3^0[/tex] = p which makes p equal to $27,765.29.
PART BTo solve for the PART B answer
the formula for continuous compounding is:
[tex]f = p * e^(r*n)[/tex]
Where
r is the interest rate per time period which is in years.n is the number of time periods which is in years.The formula becomes:
[tex]120,000 = p * e^(.048 * 30).[/tex]
divide both sides of this equation by [tex]3^(.048 * 30)[/tex] to get:
[tex]120,000 / (e^(.048*30))[/tex] = p which makes p equal to $28,431.33.
#SPJ1
Read more about compound interest here:
https://brainly.com/question/24274034
i need a an A pls help
Answers
Answer:
it B
Step-by-step explanation:
B stands for ben
like talking ben?
Answer:
c. 7x-2=19
Step-by-step explanation:
1. add 2 to both sides 7x-2(+2)=19+2
2. divide by 7 on both sides7x/7=21/7
3. x=3
If a bank offers to double your money in 8 years, what is the effective rate of interest?
Answers
Answer:
I think I would be 16 cause if 8 double it is 16
(23/7+61/3)_34/3
what the answer
Answers
so the lcm of 7 and 3 is 21
So 23*3 + 61*7 divide the whole by 21 which is 7*3
The answer will come out to 496/21
Then outside the bracket the whole is times 34/3
So 34/3*496/21=
16864/64
We can’t simplify it more so that’s the answer
Determine the unknown side of the similar
triangle.
3 in
4 in
Q
12 in
Answers
Answer:
Q=9
Step-by-step explanation:
if we get the bottom lengths of both triangles and divide them by eachother we can find the scale factor. so 12/4=3 meaning the scale factor is 3 meaning the bigger triangle is 3 times bigger so if we have the smaller version of the length of Q we just have to multiply 3 by 3 to get the enlarged version so Q=9inch
(its a lot of words but i wanted to make sure you understand)
The results of a poll show that between 74% and 82% of consumers prefer Chip A to Chip B. What is the point estimate for the percent of consumers that prefer Chip A to Chip B?
74%
78%
82%
8%
Answers
Answer:
78%
Step-by-step explanation:
First of all, the point estimate is a value located in between the upper confidence limit and the lower confidence limit, it identifies a point in some parameter space.
This question provides us with an interval estimate which is a range of values used to estimate a population parameter.
Interval Estimate = 74% to 82%
74% = Lower confidence limit
82% = Upper confidence limit
Point estimate = middle value
= [tex]\frac{74+82}{2}=\frac{156}{2}[/tex]
= 78%
What is the value of the discriminant for the equation 0=2x^2+x-3?
Discriminant = b^2-4ac
A.-25
B.-23
C.25
D.26
Answers
Answer: 25
Step-by-step explanation: The quadratic equation may be expressed in a form, ax² + bx + c =0. From the given equation, a = 2, b = 1, and c = -3. Substituting these value to the equation of the discriminant (D).
D = b² - 4ac
D = 1² - (4)(2)(-3) = 25
Thus, the discriminant of the equation of 25.
What is the measure of angle x?
Answers
Answer:
The answer is 47°
Step-by-step explanation:
Total angles in a triangle is 180°
so 31+x+102 = 180
x= 180-133
x=47°
PLEASE HELP ME WITH THIS!!!!
Answers
Answer:
Triangles A and B
Step-by-step explanation:
Similar triangles have congruent corresponding angles. Triangles a and b both have angle measures of 90°, 23° and 67°. Triangle C has different angle measures therefore it cannot be similar to either triangle A and B.
Similar triangles also have similar side length ratios via corrsesponding sides. This is true for triangles A and B eg. have corresponding side length ratios of 24/12 , 26/13 and 10/5 which all equal 2
So we can conclude triangles A and B are similar