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Exam 4 for Calculus and Analytical Geometry - Spring 2005 | MAT 250, Exams of Analytical Geometry and Calculus

Murray State UniversityAnalytical Geometry and Calculus

Material Type: Exam; Class: Calculus and Analytical Geometry I; Subject: MAT Mathematics; University: Murray State University; Term: Unknown 1989;

Typology: Exams

Pre 2010

Uploaded on 08/17/2009

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Spring ’05/MAT 250/Exam 4 Name: Show all your work.
1. (5pts) Find fif f0(x) = e4x+ 5 sin xand f(0) = 2.
2. (10pts) Evaluate using the Fundamental Theorem of Calculus, part 2:
a) Z8
4
1
2xdx =
b) Z16
9
√x dx =
3. (2pts) If R3
−1f(x)dx = 5 and R6
−1f(x)dx = 12, how much is R6
3f(x)dx?
pf3
pf4

Partial preview of the text

Download Exam 4 for Calculus and Analytical Geometry - Spring 2005 | MAT 250 and more Exams Analytical Geometry and Calculus in PDF only on Docsity!

Spring ’05/MAT 250/Exam 4 Name: Show all your work.

  1. (5pts) Find f if f ′(x) = e^4 x^ + 5 sin x and f (0) = 2.
  2. (10pts) Evaluate using the Fundamental Theorem of Calculus, part 2:

a)

4

2 x

dx =

b)

9

x dx =

  1. (2pts) If

− 1 f^ (x)^ dx^ = 5 and^

− 1 f^ (x)^ dx^ = 12, how much is^

3 f^ (x)^ dx?

  1. (2pts) Simplify using part 1 of the Fundamental Theorem of Calculus:

d dx

∫ (^) x

1

√ (^3) t (^2) + t − 1 dt =

  1. (4pts) Use properties of integrals to show that π ≤

∫ (^) π/ 2

−π/ 2

2 − cos^2 x dx ≤ 2 π.

  1. (5pts) Use the “area” interpretation of the integral to find

− 2 (2x^ −^ 2)^ dx.^ Draw a picture.

  1. (4pts) Use a graph to determine whether

0

e−x

2 −

dx is positive or negative. Explain

your reasoning.

  1. (4pts) Suppose the rabbit population in a certain forest is 123 rabbits at time t = 0 and increases at rate r(t) = 3 + et, t in years. How many rabbits are there at the end of year 4?

Bonus. (5pts) The graph of a function f is drawn below. Sketch the graph of the antideriva- tive F of f if we know that F (0) = 4.

a b c