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This problem has two parts, both of which require written work

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This problem has two parts, both of which require written work. Submit work for this
problem to D2L.

- : 1 omtnin ff
Consider the function f(z) = hie Calculate the derivative f’ (a) below and show your work

zr
on D2L.
1 ne / ie ft
a. For f(z) = Bea the derivative (found using your preferred technique) is f’(z) =
xc
b. Apply the limit definition of the derivative to calculate the derivative of f(x) = ben
x

This problem has two parts, one online and one on paper. Submit work for this problem to
D2L.
Consider the function f(z) = zx? — 3x — 2. Submit work from parts a. - d. on D2L.
a. The derivative is f’(z) = Ea
b. The second derivative is f"” (x) = 33
c. List ordered pairs (e.g., (c, f(c))) that give the locations of all critical points
if you have more than one point on the graph, separate each by a comma
d. List ordered pairs (e.g., (c, f(¢))) that give the locations of all possible inflection points
if you have more than one point on the graph, separate each value by a comma.

This problem has two parts, one online and one on paper. Submit work for this problem to
D2L.
- . a; 8r
Consider the indefinite integral | —————— dz.
(5 — 7x?)
a. This problem requires u-substitution, enter u:
us iti
b. Define the differential du:
du =( He) da
c. In terms of w, enter the integrand that substitution gives (all constants should stay inside
the integral for now):
/ du
Hint: use the ‘Preview My Answers’ button to check the format of your answer before
submitting.
d. Give the final value of the indefinite integral:
82 a
——_ dz = 3st
(5 — 7x?)
Hint: use the ‘Preview My Answers’ button to check the format of your answer before
submitting.

You are not asked to submit written work for this problem. Enter your answers here.
Consider the function f(z) = 2* + 2? — 82 — 12.
a. Find the derivative of f(z).
f(z) = iti
b. Calculate (and enter) the average rate of change between ry = 1 anda, = 4:
c. Calculate (and enter) the instantaneous rate of change at zp = 1.
d. Enter the equation of the tangent line to f(z) at ag = 1.
Fran(Z) =

You are not asked to submit written work for this problem. Enter your answers here.
Check the box next to all of the limits that can be calculated by direct substitution (i.e., ‘function
evaluation’).
Oo. 2-2-6
A. lim ————
a 3 z+2
co cos(z
“Ip. tim £802)
z 0 sin(z)
co 22427 —15
—¢. lim. ————_
z>2 g2 27-6
CID. lim z? + sin(rz)
z 0
co 22427 —15
— EB. lim ————_
ro3 g2—7-6
ol gz? +27 —15
— F, lim. ————_
zo2 g2—27-6

Find derivatives for each of the following functions.
a. The function is f(z) = 32? + (1+ a2)*,
f(z) =
oe 3
b. The function is g(x) =z + —,
x
g'(z) =
¢. The function is h(x) = z* cos(8 + 32°),
A'(z) =

Evaluate each of the following integrals.

a. [ox + sin(x) dx =
b 3 2,/e dz =

| oa t WvF de —
c. / 1—2+4 32? dz =

2
d. [ Qa + sin(x) dz =
0

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fall 2021 fina fall 2021 final: Problem 10

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(8 points)
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Problem 1 Suppose you are interested in various integrals corresponding to the graph of f(z) = +. Identify each of the following by the most accurate label.

Problem 2 a. LP f(z) dx |dentify your choice v

Problem 3

Problem 4 b. f Pa f(z)dzx \dentify your choice v

Problem 5

Problem 6 c. f f(x) dz Identify your choice ~

Problem 7

Problem 8 d. fr f(z) dx \dentify your choice v

Problem 9 ee met LMS Ie) 8

SEES rs Indefinite integral
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