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Statistics - Calculus - Quiz, Exercises of Calculus

Main points of this past exam are: Statistics, Probable Major, Print, Mention, Math, Calculus, Plan

Typology: Exercises

2012/2013

Uploaded on 03/31/2013

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Prof. S. Brick Math 126
Spring ’99 section 51
Calculus II; Quiz 0
1. Print your name. You must print it legibly. Also mention your year in
school and your probable major.
2. Why are you taking this course ? Will you be taking other math or statistics
courses ?
3. When and from whom did you take Calculus I ?
4. What material in Calculus I gave you the most trouble ?
5. How many hours per week do you plan to put into this class ? What will
you do if you start having difficulties with the material ?
6. Why are you taking a night course ? Are you aware that they are often
more demanding on the student ?
7. What grade do you honestly expect to get from this class ? Why ?
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Spring ’99 section 51

Calculus II; Quiz 0

  1. Print your name. You must print it legibly. Also mention your year in school and your probable major.
  2. Why are you taking this course? Will you be taking other math or statistics courses?
  3. When and from whom did you take Calculus I?
  4. What material in Calculus I gave you the most trouble?
  5. How many hours per week do you plan to put into this class? What will you do if you start having difficulties with the material?
  6. Why are you taking a night course? Are you aware that they are often more demanding on the student?
  7. What grade do you honestly expect to get from this class? Why?

Spring ’99 Calculus II; Quiz 1 section 51

  1. Print your name:
  2. Find

x x^4 + 1

dx

  1. Find

x · cos(x) dx

  1. Find

− 3

xe−x

4 dx

Spring ’99 Calculus II; Quiz 3 section 51

  1. Print your name:
  2. Find

x + 7 x^2 − x − 2

dx

  1. Using the substitution x = tan(u), find

(x^2 + 1) 52 dx

  1. How many rectangles should you use with the midpoint rule in order to approximate

the integral

0

cos(x^2 + 1) dx with an error less than 0.00001?

Spring ’99 Calculus II; Quiz 4 section 51

  1. Print your name:
  2. Find the volume of the solid obtained by rotating about the x-axis the region bounded by the curves y = tan(x) sec(x), the x-axis, x = 0 and x = π/4.
  3. Find the volume obtained by rotating about the y-axis the region bounded by y = ex, the x-axis, x = 0 and x = 1.
  4. Find the arc-length of the section of the curve y =

x

2 (^3) from x = 0 to x = 1

Spring ’99 Calculus II; Quiz 6 section 51

  1. Print your name:
  2. Show that y = xex^ is a solution to y′′^ − 2 y′^ + y = 0
  3. Find the centroid of unit quarter-circle y =

1 − x^2 for 0 ≤ x ≤ 1.

  1. For what value of K is f (x) =

K

1 + x^2

for 0 ≤ x ≤ +∞ a probability distribution?

Spring ’99 Calculus II; Quiz 7 section 51

  1. Print your name:
  2. Determine whether or not the sequence an =

n · ln(n) n^2 + 1

converges. If it converges, find

its limit.

  1. Find the sum 12 − 14 + 18 − 161 + 321 − 641 +...
  2. The Fibonacci sequence can be defined by a 1 = a 0 = 1 and an+1 = an + an− 1 for n ≥ 1. It is easy to see that it diverges to infinity (don’t bother showing this). However,

the sequence of ratios of successive terms rn =

an+ an

converges. Find its limit.

Spring ’99 Calculus II; Quiz 9 section 51

  1. Print your name:
  2. Find the radius of convergence of the power series

n=

enxn.

  1. Find a power series for y =

4 − x

. For what x does it converge?

  1. Find the Taylor series for y = e−x

2 and use the first three terms to approximate the

integral

0

e−x

2 dx.

Spring ’99 Calculus II; Quiz 10 section 51

  1. Print your name:
  2. Find the Maclaurin series for ex, cos(x), and sin(x).
  3. Find a power series for y =

3 x (1 + 2x)^1 /^2

  1. Use power series to find the Taylor polynomial P 4 of the solution to the initial value problem y′^ + y = 2x + x^2 with y(0) = 1.