Calculus Exam

1 Dr. Kim Barnette MA 151 Spring 2019

Name:

February 18, 2019 MA 151-02 Spring 2019 Linear Algebra

Take Home Exam #1 – Questions will be posted on Blackboard by Monday, February 18th. I will send an announcement via Blackboard (to your udc.edu email) once posted.

SHOW ALL OF YOUR WORK (use additional sheets of paper if necessary)

The exam will be due at 2:00pm in class on Monday, February 25, 2019.

ATTACH THIS COVER SHEET TO YOUR EXAM ANSWERS

Please fill in your name and sign your name below to notify Dr. Barnette and UDC that you followed this mandatory requirement:

I, _____________________________, attest and confirm that I did not collaborate with anyone on this Take Home Exam. I only used my MA 151 textbook references, presentation handouts posted on Blackboard, or class notes/assignments to complete this MA 151 Take Home Exam.

__________________________________________ _________________ Signature Date

(please see following pages 2 through 4 for exam questions; there are 3 exam questions; each question has multiple parts)

SHOW ALL OF YOUR WORK (use additional sheets of paper if necessary)

2 Dr. Kim Barnette MA 151 Spring 2019

1. (worth 40 points) Evaluate the limits of the following functions, f(x), as x approaches c. If the limit does not exist at c, redefine the function algebraically and state whether c is a removable or nonremovable point of discontinuity.

a. f(x) = 10x / (20x2 + 15x) as x approaches 0.

b. f(x) = (1/3)2x as x approaches –1.

c. f(x) = (6x2 + x – 1) / (1 – 3x) as x approaches 1/3.

d. f(x) = (x – 3) / (x + 2) as x approaches 2.

e. f(x) = (x2 + x – 56) / (x2 – 13x + 42) as x approaches 7.

f. f(x) = (–3x + x2 – 10) / (–x2 – 10 – 7x) as x approaches –2.

g. f(x) = 2x – 1 as x approaches 2.

h. f(x) = (√(3 + x) - √(3)) / x as x approaches 0. (√ is the square root symbol)

3 Dr. Kim Barnette MA 151 Spring 2019

2. (worth 35 points) Determine whether the limits exist by evaluating one-sided limits of the following function:

f(x) = |x|/x as x approaches 0 from the left and from the right (Note: |x| is the absolute value of x)

a. Graph the function (either sketch it on paper or attach a screenshot of the graph sketched in www.desmos.com)

b. What is the limit of f(x) as x approaches 0– ?

c. What is the limit of f(x) as x approaches 0+ ?

d. Cite the theorem that discusses whether the limit of a function exists at a given point based on the one-sided limits at that point.

e. Is f(x) continuous at 0?

f. Is 0 a removable or nonremovable point of discontinuity?

4 Dr. Kim Barnette MA 151 Spring 2019

3. (worth 25 points) Determine whether the limits exist by evaluating one-sided limits of the following function:

f(x) = (x + 2) / (x – 2) as x approaches 2 from the left and from the right

a. Graph the function (either sketch it on paper or attach a screenshot of the graph sketched in www.desmos.com)

b. What is the limit of f(x) approaching as x approaches 2– ?

c. What is the limit of f(x) approaching as x approaches 2+ ?

d. Does the limit of f(x) exist at x = 2?

e. With regards to f(x) = (x + 2) / (x – 2), what is x = 2? (circle all that apply)

i. Vertical asymptote

ii. Removable point of discontinuity

iii. Nonremovable point of discontinuity

iv. Point of continuity