This

**preview**shows page 1. to view the full**4 pages of the document.**Final practice problems for Calculus I Fall 2007

x Q(x)Q0(x)Q00(x)

0 1 −4−3

1 2 0 7

2 0 −5 2

3 1 0 −2

4 5 5 −2

5 8 −1 0

6−2 2 3

7−2 0 0

1. Suppose Qand its ﬁrst derivative Q0and its second de-

rivative Q00 have the values indicated in the accompanying

table.

Below are some disconnected pieces of the graph of Q. Each

value of xmatches exactly one picture. Find the matches.

A B C D E F G H

2. The line y= 3x+ 7 is tangent to the graph of y=f(x) at x= 4. What is f(4)? What is

f0(4).

3. Suppose yis deﬁned implicitly as a function of xby x2+Axy2+By3= 1 where Aand

Bare constants to be determined. Given that this curve passes through the point (3,2) and

that its tangent at this point has slope −1, ﬁnd Aand B.

4. Evaluate these indeﬁnite integrals.

a) Z7x2−3ex+5

xdx b) Z(x3+5)2dx c) Z5 sin x+cos(5x)dx d) Zx

x2+ 5 dx

5. Evaluate these deﬁnite integrals using methods of calculus.

a) Z2

1x3−1

x4dx b) Zln 3

0

4e2xdx c) Z2

0

x2√1+3x3dx d) Zln 2π

ln π

exsin(ex)dx

e) Zee

e

1

xln xdx

6. Find dy

dx.

a. y=x(x2)b. y=3x+ 5

7x2+ 1 c. y= ln(3x+ 5) d. xey= cos(xy)

###### You're Reading a Preview

Unlock to view full version