Download Calculus I Test I - Limits Evaluation and more Exams Calculus in PDF only on Docsity!
MA 125 00, CALCULUS I
August 26, 2010
Name (Print last name first):..........................................
Student Signature:...................................................
TEST I
No calculators are allowed!
PART I
Part I consists of questions. Clearly write your answer (only) in the space pro- vided after each question. Show all of your your work!
All problems in Part I are 6 points each
Question 1^ Evaluate the following limits.
xlim→ 2 x^2 + 3 x −x 2 −^10
Answer:.....................
Question 2
xlim→ 0 sin(7 2 xx)
Answer:.....................
Question 3
xlim→∞^ −^3 x x^34 −+ 7^5 xx^2 + 7
Answer:..................
Question 4
xlim→ 2 √^5 [sin(x)]^2 + 7
Answer:..................
Question 5
xlim→ 0 |^ xx|
Answer:.....................
Question 6
xlim→∞^ sin( xx)
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 (5.1)^3 = 132.651 and (5.01)^3 = 125.751501. If the position of a particle at time t is given by S(t) = t^3 , find:
- the average velocity v 5 , 5. 1 between times t = 5 and t = 5. 1
- the average velocity v 5 , 5. 01 between times t = 5 and t = 5. 01
- Using the above, estimate the instantaneous velocity v(5).
