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Book/movie review
22/08/2022
1:
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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