Docsity
Docsity

Prepare for your exams
Prepare for your exams

Study with the several resources on Docsity


Earn points to download
Earn points to download

Earn points by helping other students or get them with a premium plan


Guidelines and tips
Guidelines and tips

Midterm Exam MA140-01 Calculus Questions - Prof. Joe A. Stickles, Exams of Calculus

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

Pre 2010

Uploaded on 08/04/2009

koofers-user-imt
koofers-user-imt ๐Ÿ‡บ๐Ÿ‡ธ

10 documents

1 / 4

Toggle sidebar

This page cannot be seen from the preview

Don't miss anything!

bg1
MA140-01
3/4/09
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
3
( )
5
f x
x
=
โˆ’
. Using the definition of the derivative, find
'( ).
f x
2.) Given
๎˜
๎˜‚
๎˜ƒ
โˆ’>+
โˆ’โ‰คโˆ’
=
1
13
)(
2
xifkx
xifkx
xf
. Find the value of k such that
( )
f x
is continuous
everywhere.
3.) Suppose that
๎˜„
๎˜„
๎˜„
๎˜
๎˜„
๎˜„
๎˜„
๎˜‚
๎˜ƒ
โ‰ค<โˆ’
=
<<โˆ’
=
<<โˆ’+
=
424
20
20
02
021
)(
xx
x
xx
x
xx
xf .
(a) Determine
2
lim ( )
x
+
โ†’โˆ’
. (c) Determine )(lim
0
xf
xโ†’
.
(b) Determine )(lim
2
xf
xโ†’
. (d) Determine
4
lim ( )
x
f x
โˆ’
โ†’
.
pf3
pf4

Partial preview of the text

Download Midterm Exam MA140-01 Calculus Questions - Prof. Joe A. Stickles and more Exams Calculus in PDF only on Docsity!

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

f x

x

. 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 โ†’โˆ’+

. (c) Determine lim ( ) 0

f x x โ†’

(b) Determine lim ( ) 2

f x x โ†’

. (d) Determine 4

lim ( ) x

f x โ†’โˆ’

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

  • โˆ’ = โˆ’

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

f x = 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

  • bx + c will pass

through the point (1,3) and line 4x + y = 8 is tangent to the curve at the point (2, 0).