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MA 125 Final Exam: Calculus Problems, Exams of Calculus

The final exam questions for a calculus course, ma 125. The exam covers topics such as limits, derivatives, integrals, and applications of calculus. Students are required to use the given functions and equations to calculate limits, derivatives, and slopes of tangent lines.

Typology: Exams

2012/2013

Uploaded on 03/31/2013

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parveen 🇮🇳

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MA 125-06
§2.1–5.3 Final Exam score
Name:
11 December 2000
1. Use the limit definition of derivative to calculate the derivative of the function f(x) =
√x−1. (7 points)
2. A particle moving along a straight number line is observed at the follwing locations. Es-
timate the velocity of the particle at time t=3 seconds. (7 points)
time (seconds) 1 2 3 4 5
location (meters) 24 19 15 13 12
3. Determine where the given function is continuous. Explain fully. (7 points)
f(x) =
0 for x<0
3xfor 0 ≤x<2
sin(πx) +5 for x≥2
pf3
pf4
pf5

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Download MA 125 Final Exam: Calculus Problems and more Exams Calculus in PDF only on Docsity!

MA 125-

Final Exam

score

Name:

11 December 2000

  1. Use the limit definition of derivative to calculate the derivative of the function√ f (x) = x − 1. (7 points)
  2. A particle moving along a straight number line is observed at the follwing locations. Es- timate the velocity of the particle at time t = 3 seconds. (7 points)

time (seconds) 1 2 3 4 5 location (meters) 24 19 15 13 12

  1. Determine where the given function is continuous. Explain fully. (7 points)

f (x) =

0 for x < 0 3 x for 0 ≤ x < 2 sin (π x) + 5 for x ≥ 2

  1. Evaluate the following limits if they exist. Give reasons where appropriate. (5 points each)

(a)lim x → 2 −

tan x (x − 2 )^3

(b)lim x → 0

[[x]] x

  1. Let C be the curve in the xy -plane described by the parametric equations x(t) = cos t and y(t) = 2 sin t. Find a formula, in terms of t , for the slope of the tangent line. Then determine all points on the curve that have a tangent line with slope −2. (7 points)
  2. Let h 1 (x) = f (g(x)) , h 2 (x) = f (x) · g(x) , and h 3 (x) = f (x)g(x). Use the information in the table to find the value of h ′ 1 ( 3 ) , h ′ 2 ( 3 ) , and h ′ 3 ( 3 ). (7 points)

x 1 2 3 4 5 f (x) 5 2 1 3 1 f ′ (x) 2 1 2 2 3 g(x) 3 2 4 3 1 g ′ (x) 3 2 3 2 3

  1. Evaluate the following limits. Show your work and explain as needed. (5 points each)

(a)lim x → 0

e^2 x^ − 1 sin x

(b)lim x →∞ ln ln √ x x

  1. A right triangle has vertices (0,0), (3,0), and (0,5). Find the area of the largest rectangle that can be inscribed in the triangle if two edges of the rectangle are along the legs of the triangle. (8 points)
  1. Let f (x) = cos x. Draw a sketch of f (x) together with the rectangles used in the Riemann sum from x = 0 to x = π 2 based on left endpoints with 4 subinter- vals. Then use your calculator to com- pute the values of the left sums using 4, 10, and 50 rectangles. (7 points)
  2. A particle has a velocity function of v(t) =

1 + t^2

. If the particle begins at x = 10 when t = 0, where will it be located at t = 1 and t = 10? (Approximate your answers to two decimal places.) (7 points)