MATH 121 Final: MATH 121 Amherst S13M121Final
15 Feb 2019
School
Department
Course
Professor
MATHEMATICS 105 FINAL EXAMINATION DECEMBER 20, 2011
200 Points 3 Hours Show All Work
Do all work in the blue books provided. Do not write on the test paper. Mark your answers
clearly, and write down all steps used to obtain your answers.
1. [20 Points] Compute the following derivatives. Do not simplify your answers.
(a) d
dt at3+b
ct2+d, where a, b, c, d are constants
(b) d
dxp1 + (x2−1)3
(c) d2
dx2x(1 + x)6
2. [10 Points] Simplify the answer to part (c) of Problem 1 as much as possible.
3. [20 Points] Evaluate the following limits. Please justify your reasoning.
(a) lim
x→2
x2−4x+ 4
x2+ 3x−10
(b) lim
x→∞
x2−4x+ 4
x2+ 3x−10
(c) lim
x→1
x−√2−x
x−1
(d) lim
x→1
x− |2−x|
x−1
4. [10 Points] Find the equation of the line tangent to the curve y=(x+ 1)3
(3 −x)2at the
point where the x-coordinate is 1.
5. [10 Points] Suppose we know that lim
h→0f(2 + h) = 3.
(a) Compute lim
x→2f(x) and explain your reasoning.
(b) Is f(2) = 3? Explain your reasoning.
6. [10 Points] Compute f′(x) for f(x) = x−1
x+ 1 using the limit definition of derivative.
7. [15 Points] Find the absolute minimum and maximum values of the function
f(x) = x(x2−7)3
on the interval 0 ≤x≤3.
1
Document Summary
Do all work in the blue books provided. Mark your answers clearly, and write down all steps used to obtain your answers: [20 points] compute the following derivatives. 1: [15 points] rain is falling in a storm that intensi es over time. Give reasons: [20 points] we have a rectangular box with square base whose edges are changing with respect to time. We will assume that the edges of the base are increasing at a rate of. 2 in/min and the height is shrinking at a rate of 3 in/min. A fence down the middle is needed to keep the species apart (they don"t get along). The zoo has a total of 1200 ft of fence for the project. What is the greatest total area that can be enclosed: [20 points] do a complete curve graphing for y = x +
