






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
Material Type: Exam; Class: Calculus I; Subject: Math; University: Portland Community College; Term: Winter 2009;
Typology: Exams
1 / 10
This page cannot be seen from the preview
Don't miss anything!
MTH 251 – Final Exam – No Calculator
Given March 18, 2009 Name
Please note that this test counts for 125 points
that is, do not show steps on this problem. (2 points each)
d (^) x x e dx
= b.
d 4
d (^) 3 t dt
2 sin
d x dx
d (^) 3 x e dx
2 cos
d w dw
g. (^5)
d 1
dx e
h.
ln 8
d
dx x
d
d
j. 1
d x
dx x
d
d
d e dt
3 3
f x x x
= −. Show all necessary work in a
manner consistent with that illustrated and discussed during lecture.
y
the tangent line to this curve at the point (^) ( 0,0 (^) ). Make sure
that your work is well organized and that your conclusion is
clear. (18 points)
Figure 1
sin 2 4
2
x
y x
. Find the
equation of the tangent line to this curve at the point (^) ( −2, − (^1) ).
Make sure that your work is well organized and that your
conclusion is clear. (18 points)
Figure 2
intercepts, points of discontinuity, and points of nondifferentiability are directly implied by the
stated properties.
5
lim 3 x − f^ x → −
5
lim 2 x
x
f x → ∞
1 2 y x tan x ln x 1
− = − +. Show your work.
Figure 4
( ) 3 2 4
x f x x
is (^) ( )
( )
( )
(^2 )
x f x x x
.
a. List the critical numbers of f ; no explanation nor sentence required.
b. Build an increasing/decreasing table for f. Make sure that you include the details
illustrated and discussed during lecture.
c. State the local minimum points and local maximum points that occur on f.
you find each of the following. (16 points total)
a. Find the value of (^) ( ( 4 ))
d g dx
if g (^) ( x ) (^) = f (^) ( x ).
b. Find the value of h ′^ ( 4 )if (^) ( ) ( )
2 h x = ⎡⎣ f x ⎤⎦.
c. Find the value of ( 6, 6)
dy
dx
along the curve (^) ( )
2 y = x f x.
Table 1
x f^ ( x^ ) f^ ′( x )
1 0 5
2 4 4
3 7 3
4 9 1
(^5 8) − 3
(^6 6) − 4
7 3 − 5