Question 1

Estimate the sum of   to within 0.01.

Accepted Answer

A)  0.10 
B)  2.00 
C)  1.97 
D)  0.03 
A)  0.10 
B)  2.00 
C)  1.97 
D)  0.03

Question 2

A dosage of 50 mL of a drug is given at times   . The drug decays exponentially with rate 0.6 in the bloodstream. The amount in the bloodstream after   doses is   Find the eventual level of the drug (after an "infinite" number of doses). Round to the nearest mL.

Accepted Answer

A)  83 mL 
B)  125 mL 
C)  111 mL 
D)  152 mL 
A)  83 mL 
B)  125 mL 
C)  111 mL 
D)  152 mL

Question 3

Determine how many terms are needed to estimate   to within 0.0001.

Accepted Answer

A)  k = 5 
B)  k = 6 
C)  k = 5,000 
D)  k = 50,000 
A)  k = 5 
B)  k = 6 
C)  k = 5,000 
D)  k = 50,000

Question 4

Determine if   is absolutely convergent, conditionally convergent or divergent.

Accepted Answer

A)  absolutely convergent 
B)  conditionally convergent 
C)  divergent 
A)  absolutely convergent 
B)  conditionally convergent 
C)  divergent

Question 5

Determine whether   converges or diverges. Show all your work.

Accepted Answer

@#IMG-DLM& ; the lim

Question 6

Estimate the error in using   to approximate the sum of   . Show all your work.

Accepted Answer

Answers may vary.
Let @#IMG-DLM& . Since

Question 7

Estimate the sum of   to within 0.01.

Accepted Answer

A)  3.84 
B)  3.75 
C)  3.79 
D)  -0.25 
A)  3.84 
B)  3.75 
C)  3.79 
D)  -0.25

Question 8

Write   as a fraction.

Accepted Answer

A)    
B)    
C)    
D)    
A)    
B)    
C)    
D)

Question 9

Determine if   converges or diverges. If convergent, find the sum of the series.

Accepted Answer

A)  converges with sum =   
B)  converges with sum =   
C)  converges with sum =   
D)  diverges 
A)  converges with sum =   
B)  converges with sum =   
C)  converges with sum =   
D)  diverges

Question 10

Write out terms   of the given sequence.

Accepted Answer

The answer of Write out terms   of the...

Question 11

For   , estimate the number of terms needed in a Taylor polynomial to guarantee an accuracy of   . Show all your work.

Accepted Answer

Answers may vary.
Us

Estimate the sum of to within 0.01.

A dosage of 50 mL of a drug is given at times . The drug decays exponentially with rate 0.6 in the bloodstream. The amount in the bloodstream after doses is Find the eventual level of the drug (after an "infinite" number of doses). Round to the nearest mL.

Determine how many terms are needed to estimate to within 0.0001.

Determine if is absolutely convergent, conditionally convergent or divergent.

Determine whether converges or diverges. Show all your work.

Estimate the error in using to approximate the sum of . Show all your work.

Estimate the sum of to within 0.01.

Write $Write as a fraction.$ as a fraction.

Determine if converges or diverges. If convergent, find the sum of the series.

Write out terms of the given sequence.

For , estimate the number of terms needed in a Taylor polynomial to guarantee an accuracy of . Show all your work.

Preliminaries

Limits and Continuity

Differentiation

Applications of the Derivative

Integration

Applications of the Definite Integral

Exponentials, Logarithms and Other Transcendental Functions

Integration Techniques

First-Order Differential Equations

Parametric Equations and Polar Coordinates

Vectors and the Geometry of Space

Vector-Valued Functions

Functions of Several Variables and Partial Differentiation

Multiple Integrals

Vector Calculus

Second Order Differential Equations

Filters

Exam 10: Infinite Series

Estimate the sum of to within 0.01.

A dosage of 50 mL of a drug is given at times . The drug decays exponentially with rate 0.6 in the bloodstream. The amount in the bloodstream after doses is Find the eventual level of the drug (after an "infinite" number of doses). Round to the nearest mL.

Determine how many terms are needed to estimate to within 0.0001.

Determine if is absolutely convergent, conditionally convergent or divergent.

Determine whether converges or diverges. Show all your work.

Estimate the error in using to approximate the sum of . Show all your work.

Estimate the sum of to within 0.01.

Write as a fraction.

Determine if converges or diverges. If convergent, find the sum of the series.

Write out terms of the given sequence.

For , estimate the number of terms needed in a Taylor polynomial to guarantee an accuracy of . Show all your work.

Preliminaries

Limits and Continuity

Differentiation

Applications of the Derivative

Integration

Applications of the Definite Integral

Exponentials, Logarithms and Other Transcendental Functions

Integration Techniques

First-Order Differential Equations

Parametric Equations and Polar Coordinates

Vectors and the Geometry of Space

Vector-Valued Functions

Functions of Several Variables and Partial Differentiation

Multiple Integrals

Vector Calculus

Second Order Differential Equations

Filters

Write $Write as a fraction.$ as a fraction.