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Final

# 01:640:135 Study Guide - Final Guide: Riemann Sum, Minimax, Marginal CostExam

Department
Mathematics
Course Code
01:640:135
Professor
All
Study Guide
Final

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Final practice problems for Calculus I Fall 2007
x Q(x)Q0(x)Q00(x)
0 1 43
1 2 0 7
2 0 5 2
3 1 0 2
4 5 5 2
5 8 1 0
62 2 3
72 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) Z7x23ex+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
1x31
x4dx b) Zln 3
0
4e2xdx c) Z2
0
x21+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)