Download Left Sided Limit - Calculus I - Exam and more Exams Calculus in PDF only on Docsity!
MA 125 00, CALCULUS I
August 29, 2011
Name (Print last name first):..........................................
Student Signature:...................................................
TEST I
No calculators are allowed!
PART I
Part I consists of eight questions. Clearly write your answer (only) in the space provided after each question. Show all of your your work for full credit!
All problems in Part I are 6 points each.
Question 1^ Evaluate the following limits.
xlim→ 3 x^2 + x −x^ − 3 12
Answer:.....................
Question 2
xlim→ 0 sin(5sin(2xx))
Answer:.....................
Question 3
xlim→∞^ −^5 x x^36 + 4− 5 xx^2 −^5
Answer:..................
Question 4
xlim→ 0 cos(ln(x^2 + 1))
Answer:..................
Question 5
xlim→ 0 − |^ xx|. Note this is a left-sided limit.
Answer:.....................
Question 6
xlim→ 01 x
Answer:........................
PART II
Part II consists of 3 problems. You must show correct reasons to get full credit. Displaying only the final answer (even if correct) without the relevant steps will not get full credit.
Problem 1 (18 points)
Given the graph of the function y = f (x) below find:
- (^) x→−lim 1 − f (x) =
- (^) x→−lim 1 + f (x) =
- (^) xlim→− 1 f (x) =
- (^) xlim→ 2 − f (x) =
- (^) xlim→ 2 + f (x) =
- (^) xlim→ 2 f (x) =
- (^) xlim→∞ f (x) =
- State all intervals on which f (x) is continuous.
Problem 2 (18 points)
You may use that(5.01)^2 = 25.1001. If the position of a particle at time t is given by S(t) = t^2 (meters; time in seconds), find:
- the average velocity v 5 , 5. 1
- the average velocity v 5 , 5. 01
- Using a limit argument, obtain the instantaneous velocity v(5). You must explain your answer!!
