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1. Compute the first, second, and third derivative of a. f(x) = x² In(x+1) b. h(x) = x² sin x

1. Compute the first, second, and third derivative of a. f(x) = x² In(x+1) b. h(x) = x² sin x

Calculus: Early Transcendentals
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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1. Compute the first, second, and third derivative of a. f(x) = x² In(x+1) b. h(x) = x² sin x %3D 2. Let ах+b f(x) = { ax + x + 2 b x> -1 X< -1 Find the values of a and b such that f is differentiable on R. 3. Compute f(x+h) - f(x) and lim f (x+h) – f(x) for the following functions: h→0 a. f (x) = sin x b.g (x) - 2 %3D 4. A particle is moving in a straight line and its distance s, in meters, from a fixed point in the line after t seconds is given by the equation, s(t) = 12 t - 15 t2 +4 t3 a. Find the velocity of the particle after 3 seconds. %3D b. Find the acceleration at time t = 3
Transcribed Image Text:1. Compute the first, second, and third derivative of a. f(x) = x² In(x+1) b. h(x) = x² sin x %3D 2. Let ах+b f(x) = { ax + x + 2 b x> -1 X< -1 Find the values of a and b such that f is differentiable on R. 3. Compute f(x+h) - f(x) and lim f (x+h) – f(x) for the following functions: h→0 a. f (x) = sin x b.g (x) - 2 %3D 4. A particle is moving in a straight line and its distance s, in meters, from a fixed point in the line after t seconds is given by the equation, s(t) = 12 t - 15 t2 +4 t3 a. Find the velocity of the particle after 3 seconds. %3D b. Find the acceleration at time t = 3
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