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Problem 1. For every real number a, compute the derivative of y = x4 at x = a as a limit of a difference quotient. Show your work.

Problem 1. For every real number a, compute the derivative of y = x4 at x = a as a limit of a difference quotient. Show your work.

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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Problem 1. For every real number a, compute the derivative of y = x4 at x = a as a limit of a difference quotient. Show your work. Problem 2. For every real number a # 0, for every nonnegative integer n, for the function f(x) x^, simplify the limit, I lim q→1 f(q. a) – f(a) - (q. a) — a - Evaluate your simplified limit using the formula for a finite geometric sum, q" - 1 9-1 1+q+q² + ··· + q-1 ... Use this to compute f'(a) for a 0. =
Transcribed Image Text:Problem 1. For every real number a, compute the derivative of y = x4 at x = a as a limit of a difference quotient. Show your work. Problem 2. For every real number a # 0, for every nonnegative integer n, for the function f(x) x^, simplify the limit, I lim q→1 f(q. a) – f(a) - (q. a) — a - Evaluate your simplified limit using the formula for a finite geometric sum, q" - 1 9-1 1+q+q² + ··· + q-1 ... Use this to compute f'(a) for a 0. =
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