01:640:135 Study Guide - Final Guide: Riemann Sum, Minimax, Marginal CostExam
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Final practice problems for Calculus I Fall 2007
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
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
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.
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.
x4dx b) Zln 3
4e2xdx c) Z2
x2√1+3x3dx d) Zln 2π
6. Find dy
a. y=x(x2)b. y=3x+ 5
7x2+ 1 c. y= ln(3x+ 5) d. xey= cos(xy)
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