# Limits and Continuity Questions and Answers

Math

Limits and ContinuityFind all points where the function is discontinuous.
A. None
B. x=2
C. x = 4
D. x = 4, x = 2

Math

Limits and ContinuityLet f(x) = -8 - 5/x+16
Complete the tables below. Round all table values to four decimal places, if necessary. Enter DNE if a function value is undefined.
Using the data in the tables above, determine the following limits. Enter DNE if a limit fails to exist, except in case of an infinite limit. If an infinite limit exists, enter ∞ or -∞, as appropriate.

Math

Limits and ContinuityLet f(x)=√x6 +5x - x³ - 3.
Complete the tables below. Round all table values to four decimal places, if necessary. Enter DNE if a function value is undefined.
Using the data in the tables above, determine the following limits. Enter DNE if a limit fails to exist, except in case of an infinite limit. If an infinite limit exists, enter ∞ or -∞, as appropriate.

Math

Limits and Continuity(1 point) Find an integer which is the limit of
tan(8x)/2x
as x goes to 0. (Enter I for infinity or DNE for does not exist.)

Math

Limits and ContinuityUse a graph or table of values near x =π/2 to estimate the value of this limit:
lim
x - 72
cos(7x)/x-π/2
i

Math

Limits and ContinuityLet f be the function defined as
f(x)= 3 for x<5
x+7 for x≥ 5
Which of the following statements is true?
f is not differentiable at x = 5 because f is not defined at x = 5.
f is not differentiable at x = 5 because fis not continuous at x = 5.
f is not differentiable at x = 5 because the graph off has a vertical tangent at x = 5.
f is not differentiable at x = 5 because the graph of f has a cusp at x = 5.

Math

Limits and ContinuityFind the value or values of c that satisfy the equation f(b)-f(a) / b-a = f'(c) in the conclusion of the mean value theorem for the given function and interval.
f(x)=10x+10/x , [1/8,8]
c=
(Use a comma to separate answers as needed.)

Math

Limits and ContinuityDetermine the domain and range of the following parabola.
Select the correct answer below:
f(x) = -(x + 5)² - 4
Domain is all real numbers. Range is f(x) ≥ -5
Domain is all real numbers. Range is f(x) ≤ -5
Domain is all real numbers. Range is f(x) ≥-4
Domain is all real numbers. Range is f(a) ≤-4

Math

Limits and ContinuityUse the Direct Comparison Test to determine the convergence or divergence of the series.
∞
Σ 8^n/(9^n) +7
n=0
a)converges
b)diverges

Math

Limits and ContinuityIn a study on the speed of muscle contraction in a certain species of frogs under various loads, researchers found that the speed of contraction decreases with increasing loads. In particular, they found that the relationship between speed of contraction v (in centimeters per second) and load x (in grams) is given approximately by v(x) = 29+0.05x/x, x≥5
(A) What does v(x) approach as x increases?
(B) Sketch a graph of the function v.
(A) As x increases, v(x) approaches

Math

Limits and ContinuityYou want to be able to withdraw $25,000 from your account each year for 25 years after you retire. You expect to retire in 30 years. If your account earns 5% interest, how much will you need to deposit each year until retirement to achieve your retirement goals?

Math

Limits and ContinuityGiven a continuous function f(x) with f(-5) = - 1 and f(9) = - 8:
There must be a number c with − 5 < c < 9 and f(c) = - 4.6.
There might be a number c with - 5 < c < 9 and f(c) = - 4.6.
There cannot be a number c with -5 < c < 9 and f(c) = - 4.6.

Math

Limits and ContinuityUse the graph of the function f shown to estimate the following limits and the function value. Complete parts (A) through (D).
(C) Find the limit lim x⇒1 f(x).
Select the correct choice below and, if necessary, fill in the answer box to complete your choice.
A. lim x⇒1 f(x)
B. The limit does not exist.
(D) Find the function value f(1).
A. f(1) =
B. The function does not have a value.

Math

Limits and ContinuityGiven a function f(x) with f(− 8) = 1 and f(9) ,m= 2:
There must be a number c with -8 < c < 9 and f(c) = 1.4.
There might be a number c with 8 < c < 9 and f(c) = 1.4.
There cannot be a number c with -8 < c < 9 and f(c) = 1.4.

Math

Limits and ContinuitySuppose that a ball is rolling down a ramp. The distance traveled by the ball is given by the function s(t), where t is the time, in seconds, after the ball is released, and s(t) is measured in feet. For the given function, find the ball's average velocity from t₁ to t₂.
s(t) = 12t²; t₁ = 5, t₂ = 5.001
A. 0.12 ft/sec
B. 12.012 ft/sec
C. 120.012 ft/sec
D. -120.012 ft/sec)

Math

Limits and ContinuityGiven the linear correlation coefficient r and the sample size n, determine the critical values for r and use your finding to state whether or not the given r represents a significant linear correlation.
Use a significance level of 0.05.
r = 0.359, n = 15
Critical values: r = 0.532, significant linear correlation
Critical values: r = 0.514, no significant linear correlation
Critical values: r = 0.514, significant linear correlation
Critical values: r = 0.532, no significant linear correlation