Practice Midterm 1 UCLA: Math 31A, Fall 2017, Exams of Calculus

This exam has 4 questions, for a total of 16 points. Please print your working and answers neatly. Write your solutions in the space provided ...

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Practice Midterm 1
UCLA: Math 31A, Fall 2017
Instructor: Jens Eberhardt
Date: 08 October 2017
This exam has 4 questions, for a total of 16 points.
Please print your working and answers neatly.
Write your solutions in the space provided showing working.
Indicate your final answer clearly.
You may write on the reverse of a page or on the blank pages found at the back of the booklet however
these will not be graded unless very clearly indicated.
Non programmable and non graphing calculators are allowed.
Name:
ID number:
Discussion section (please circle):
Day/TA Allen Boozer Ben Szczesny Fan Yang
Tuesday 1A 1C 1E
Thursday 1B 1D 1F
Question Points Score
1 4
2 4
3 4
4 4
Total: 16
pf3
pf4
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Practice Midterm 1

UCLA: Math 31A, Fall 2017

Instructor: Jens Eberhardt Date: 08 October 2017

  • This exam has 4 questions, for a total of 16 points.
  • Please print your working and answers neatly.
  • Write your solutions in the space provided showing working.
  • Indicate your final answer clearly.
  • You may write on the reverse of a page or on the blank pages found at the back of the booklet however these will not be graded unless very clearly indicated.
  • Non programmable and non graphing calculators are allowed.

Name:

ID number:

Discussion section (please circle):

Day/TA Allen Boozer Ben Szczesny Fan Yang Tuesday 1A 1C 1E Thursday 1B 1D 1F

Question Points Score

1 4 2 4 3 4

4 4 Total: 16

  1. Consider the following function

f (x) =

x^2 + x + 1 if x ≤ 3 √ 6 x + 7 if x > 3.

(a) (2 points) Using the limit laws, determine the left-hand and right-hand limit of f (x) at x = 3. (b) (1 point) Does the limit of f (x) at x = 3 exist? (c) (1 point) Is f (x) continuous at x = 3? If not, which type of discontinuity does it have?

  1. Consider the function f (x) = x^3 + 1 (a) (3 points) Compute f ′(1) using the definition of the derivative. You are not allowed to use the power rule! (b) (1 point) Determine the equation of the tangent line of f (x) at x = 1.
  1. Compute the following derivatives. You may use all rules learned so far.

(a) (2 points) d

2 dx^2 (3x

(^3) + 4x (^2) + 2x − 1)

(b) (2 points) (^) dxdx

(^2) + 2 x

This page has been left intentionally blank. You may use it as scratch paper. It will not be graded unless indicated very clearly here and next to the relevant question.