Area functions and the Fundamental Theorem Consider the function f ( t ) = { t i f − 2 ≤ t < 0 t 2 2 i f 0 ≤ t ≤ 2 and its graph shown below . Let F ( x ) = ∫ − 1 x f ( t ) d t and ∫ − 2 x f ( t ) d t . 56. a. Evaluate G (−1) and G (1). b. Use the Fundamental Theorem to find an expression for G′ ( x ), for −2 ≤ x ≤ 0. c. Use the Fundamental Theorem to find an expression for G′ ( x ), for 0 ≤ x ≤ 2. d. Evaluate G′ (0) and G′ (1). Interpret these values. e. Find a constant C such that F ( x ) = G ( x ) + C .
Area functions and the Fundamental Theorem Consider the function f ( t ) = { t i f − 2 ≤ t < 0 t 2 2 i f 0 ≤ t ≤ 2 and its graph shown below . Let F ( x ) = ∫ − 1 x f ( t ) d t and ∫ − 2 x f ( t ) d t . 56. a. Evaluate G (−1) and G (1). b. Use the Fundamental Theorem to find an expression for G′ ( x ), for −2 ≤ x ≤ 0. c. Use the Fundamental Theorem to find an expression for G′ ( x ), for 0 ≤ x ≤ 2. d. Evaluate G′ (0) and G′ (1). Interpret these values. e. Find a constant C such that F ( x ) = G ( x ) + C .
Solution Summary: The author evaluates the value of G(-1) and -32.
Car A starts from rest at t = 0 and travels along a straight road with a constant acceleration of 6 ft/s^2 until it reaches a speed of 60ft/s. Afterwards it maintains the speed. Also, when t = 0, car B located 6000 ft down the road is traveling towards A at a constant speed of 80 ft/s. Determine the distance traveled by Car A when they pass each other.Write the solution using pen and draw the graph if needed.
The velocity of a particle moves along the x-axis and is given by the equation ds/dt = 40 - 3t^2 m/s. Calculate the acceleration at time t=2 s and t=4 s. Calculate also the total displacement at the given interval. Assume at t=0 s=5m.Write the solution using pen and draw the graph if needed.
The velocity of a particle moves along the x-axis and is given by the equation ds/dt = 40 - 3t^2 m/s. Calculate the acceleration at time t=2 s and t=4 s. Calculate also the total displacement at the given interval. Assume at t=0 s=5m.Write the solution using pen and draw the graph if needed.
Chapter 5 Solutions
MyLab Math with Pearson eText -- Standalone Access Card -- for Calculus: Early Transcendentals (3rd Edition)
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