Student name:
Earlham College
Test 2
March 20, 2012
MATH 180: Calculus A
Spring 2012
Instructions:
Answer all questions on separate paper (not on this sheet!).
Solve all problems using algebra, except if specically indicated otherwise.
Show all solution
Student name:
Earlham College
MATH 180: Calculus A
Spring 2012
Test 1
February 7, 2012
Instructions:
Answer all questions on separate paper (not on this sheet!).
Solve all problems using algebra, except if specically indicated otherwise.
Show all soluti
Student name:
Earlham College
MATH 180: Calculus A
Spring 2012
Test 3
April 24, 2012
Instructions:
Answer all questions on separate paper (not on this sheet!).
Solve all problems using algebra, except if specically indicated otherwise.
Show all solution
Makeup Quiz 10  4/17/2012
(I) Construct a Riemann sum to approximate the area under the graph of f (x) = sin(x) + x
on the interval x = /2 to 5/2, using n rectangles with right endpoints. Final
result must be in summation notation, with all quantities c
Quiz 9  4/03/2012
(I) Find all the critical points of the function f (x) = x2 ex .
No credit for correct answers only for correct steps & reason.
(II) Sketch the graph of a continuous function that has a local minimum, but no
absolute minimums or maximum
Quiz 10  4/10/2012
(I) Find lim
+
x ln x. Show all steps.
x0
(II) Show that of all the rectangles with a given perimeter, the one wih the greatest
area is a square.
[This is part of Turnin homework: Sec. 4.6, exercise 13.]
Solution
(I) To nd lim x ln x,
Quiz 8  3/27/2012
(I) Find the derivative of y = x sin x with respect to x and simplify.
(II) The graph shows the position s of
a particle as a function of time t.
Find the intervals where it is speeding up, and where it is slowing
down. Give reasons.
s(
Quiz 7  3/06/2012
(I) Let f (x) = x 2 sin x, 0 < x 2. Find the values of x at which the tangent to
f (x) is horizontal. Show steps and reasoning.
(II) If h(x) =
f (x), nd h (2) if you are given f (2) = 4 and f (2) = 2.
Hint: This is a simpler version of
Quiz 2  1/24/2012
2ex
.
Show steps.
1 2ex
(II) Suppose the function f (t) denotes the percent of poor people in the U.S. at time t
in years. Sketch a clearlylabeled graph of f (t) between the years 19602012, and discuss whether it is onetoone (i.e.,
Quiz 5  2/21/2012
(I) Shown here is the graph of f (x), the derivative of some function f (x). Based on
this graph, answer the following questions (assume the graph continues to innity on
both ends in the direction shown):
2
1. On what interval(s) is f (
Quiz 4  2/14/2012
(I) The graph of some function y = f (x) is shown below. Sketch the graph of f (x).
You may do this directly on the graph below. Include a short discussion to explain
and justify why your graph of f (x) is the right solution.
6
4
2
3

Quiz 3  1/31/2012
(I) The graphs of f and g are given below. Use them to evaluate each of the following
limits (give a mathematical justication for your answers):
(a) lim [f (x) g(x)]
(b) lim [f (x) g(x)]
x0
(II) Find lim
x 3
1
6
2
x3 x 9
x1
using algeb
Quiz 1  1/17/2012
(I) Sketch a graph of the function
2
if x < 2
x 2,
x + 4,
if x 2
f (x) =
2x + 4, if x > 2
Graph must be neat, approximately to scale, include detailed labels, and indicate
open/closed intervals wherever needed.
(II) Use the laws of
Calculus: Mock final exam
Important Note: This mock test is not intended to be a template that your final exam will follow. The
purpose of this mock test is very simple: To give you the opportunity to practice with examquality
questions that cover the sa