


Study with the several resources on Docsity
Earn points by helping other students or get them with a premium plan
Prepare for your exams
Study with the several resources on Docsity
Earn points to download
Earn points by helping other students or get them with a premium plan
Community
Ask the community for help and clear up your study doubts
Discover the best universities in your country according to Docsity users
Free resources
Download our free guides on studying techniques, anxiety management strategies, and thesis advice from Docsity tutors
A midterm exam for a calculus course, consisting of 11 problems covering various topics such as limits, derivatives, and asymptotes. Students are required to find the limits, determine the value of constants, and apply the squeeze theorem and logarithmic differentiation.
Typology: Exams
1 / 4
This page cannot be seen from the preview
Don't miss anything!
3/4/
Page 1
Midterm Exam Calculator Portion
Will the real ________________________ please stand up?
Show all your work and explain your answers completely. I cannot give partial credit for answers that are both wrong and
unexplained. Even correct "bottom line" answers that are mysterious and unsupported will not be considered completely correct.
Show me what you are thinking. Try to keep your answers neat and organized so that I can follow them easily.
1.) Let
. Using the definition of the derivative, find (^) f '( ). x
2.) Given
2 x k if x
kx if x f x. Find the value of k such that (^) f ( ) x is continuous
everywhere.
3.) Suppose that
x x
x
x x
x
x x
f x.
(a) Determine 2
lim ( ) x
f x โโ+
. (c) Determine lim ( ) 0
f x x โ
(b) Determine lim ( ) 2
f x x โ
. (d) Determine 4
lim ( ) x
f x โโ
3/4/
Page 2
4.) Determine all vertical, horizontal, and slant asymptotes where they apply for 2 3 4 ( ). 5 1
x x f x x
Label the asymptotes.
5.) A spherical balloon is expanding. If the radius is increasing at the rate of 2 inches per minute, at what
rate is the volume increasing when the radius is 5 inches?
6.) Use logarithmic differentiation to find the derivative of
co s
x
7.) Use the Squeeze Theorem to determine the following limit.
4
0 6
lim sin x
x โ x
3/4/
Page 4
10.) The graph of y = f ( ) x is given below. From this graph, sketch a graph of y = f '( ) x on the
same set of axes.
11.) Determine coefficients a, b, and c so that the curve f(x) = ax
2
through the point (1,3) and line 4x + y = 8 is tangent to the curve at the point (2, 0).