See the attached file for questioins




Problem 2:


Find the antiderivative



Problem 3:


Find the surface area when the line segment A in the figure below is rotated about the lines:


(a) y = 1


(b) x = -2

(a)       The line segment follows the function f (x) = x + 1. The integral for the surface area of revolution is:

(a)       The line segment follows the function f (y) = y – 1. The integral for the surface area of revolution is:

Problem 4:


A sphere of radius 2 foot is filled with 2000 pounds of liquid. How much work is done pumping the liquid to a point 5 feet above the top of the sphere?

Problem 5:


Find the integral



Problem 6:


Find the integral



Problem 7:


Use the definition of an improper integral to evaluate the given integral:




Problem 8:


Find the indefinite integrals and evaluate the definite integrals. A particular change of variable is suggested.

Problem 9:


Evaluate the integral



Problem 10:


Evaluate the integral



Problem 11:


Evaluate the integral




Problem 12:


Show that if m and n are integers, then . (Consider m = n and

m ≠ n.)


Problem 13:


Use derivatives to determine whether the sequence below is monotonic increasing, monotonic decreasing, or neither:





Problem 14:


Each special washing of a pair of overalls removes 80% of the radioactive particles attached to the overalls. Represent, as a sequence of numbers, the percent of the original radioactive particles that remain after each washing.

Problem 15:


Calculate the value of the partial sum for n = 4 and n = 5, and find a formula for sn. (The patterns may be more obvious if you do not simplify each term.)

Problem 16:


In the proof of the Integral Test, we derived an inequality bounding the values of the partial sums  between the values of two integrals:



Problem 17:


Use any of the methods learned from this MATH141 class to determine whether the given series converge or diverge. Give reasons for your answers.



Problem 18:


 Determine whether the given series Converge Absolutely, Converge Conditionally, or Diverge, and give reasons for your conclusions.



Problem 19:


Find the interval of convergence for the series below. For x in the interval of convergence, find the sum of the series as a function of x. (Hint: You know how to find the sum of a geometric series.)



Problem 20:


Represent the integral as a numerical series:




Use the series representation of these functions to calculate the limits.



Determine how many terms of the Taylor series for f(x) are needed to approximate f to within the specified error on the given interval. (For each function use the center c = 0.)


             within 0.001 on [-1, 4].



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