Math 161 Name:
Final
May 2, 2017 Section:
Show your work, use calculus and proper notation for full credit.
Question 1 2 3 4 5 6 7 8 9 10 11 12 13 14 Total
Points 5 9 6 15 16 6 6 16 10 10 10 18 15 8 150
Score
1. (5 points) Determine if the following statements are true or false. Assume all integrals and derivatives exist.
(a) T or F d
dx (f(x)g(x))=d
dx (f(x))d
dx (g(x))
(b) T or F d
dx ⇣p3⌘=3p2
(c) T or F R(4x2)dx =4R(x2)dx.
(d) T or F If lim
x!2f(x)=0 and lim
x!2g(x)=0, then lim
x!2
f(x)
g(x)does not exist.
(e) T or F Z2
1x2dx represents the area bounded by the curves f(x)=x2,y=0, x=1, and x=2.
2. (9 points) Find each of the following limits. Simplify your answer.
a) lim
x!32(x23)
(x2+3)2
b) lim
x!4
x2x12
x27x+12
c) lim
x!0
x+1
ex
1
3. [6 points] Find the equation of the tangent line to the function f(x)=x2exat the point (1, e).
4. [15 points] Consider the function f(x) graphed below. Assume each grid line in the coordinate system corre-
sponds to one unit.
For each number a(x-value)
in the first column of the following table,
•find the function value f(a)(the y-value)
•find the indicated limits
(write DNE if they do not exist)
•indicate whether the function
is continuous at the point x=a
•indicate whether the function
is differentiable at the point x=a
a f (a)lim
x!af(x)lim
x!a+f(x)lim
x!af(x)fcontinuous fdifferentiable
-3 Yes / No Yes / No
-1 Yes / No Yes / No
1 Yes / No Yes / No
3 Yes / No Yes / No
5 Yes / No Yes / No
2
5. [16 points] Compute the derivative of the following functions. Do Not Simplify
(a) f(x)=pex3x
(b) f(x)=x2(x34)5+ln(ln x)
