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Problem1. Use the limit definition of derivative (f'(x) =_lim_ƒ(x+h)-f(x)) to calculate the derivative of the function. g(x) = 8− 3x h→0 Problem2. Find an equation of the tangent line at x = 3, assuming that f(3) = 5and ƒ'(3) = 2. 3 Problem3.. Use the limit definition of derivative (f'(x) = lim_ f(x+h)-f(x)) to compute h h→0 ƒ'(a) and find an equation of the tangent line. 1. f(t) = t – 2t², a = 3

Problem1. Use the limit definition of derivative (f'(x) =_lim_ƒ(x+h)-f(x)) to calculate the derivative of the function. g(x) = 8− 3x h→0 Problem2. Find an equation of the tangent line at x = 3, assuming that f(3) = 5and ƒ'(3) = 2. 3 Problem3.. Use the limit definition of derivative (f'(x) = lim_ f(x+h)-f(x)) to compute h h→0 ƒ'(a) and find an equation of the tangent line. 1. f(t) = t – 2t², a = 3

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 Use the limit definition of derivative \(f'(x) = \lim\limits_{h \to 0} \frac{f(x+h) - f(x)}{h}\) to calculate the derivative of the function. \[g(x) = 8 - 3x\] ### Problem 2 Find an equation of the tangent line at \(x = 3\), assuming that \(f(3) = 5\) and \(f'(3) = 2\). ### Problem 3 Use the limit definition of derivative \(f'(x) = \lim\limits_{h \to 0} \frac{f(x+h) - f(x)}{h}\) to compute \(f'(a)\) and find an equation of the tangent line. 1. \(f(t) = t - 2t^2, \quad a = 3\) 2. \(f(x) = \sqrt{x + 4}, \quad a = 1\) 3. \(f(x) = \frac{1}{\sqrt{x}}, \quad a = 4\)
Transcribed Image Text:### Problem 1 Use the limit definition of derivative \(f'(x) = \lim\limits_{h \to 0} \frac{f(x+h) - f(x)}{h}\) to calculate the derivative of the function. \[g(x) = 8 - 3x\] ### Problem 2 Find an equation of the tangent line at \(x = 3\), assuming that \(f(3) = 5\) and \(f'(3) = 2\). ### Problem 3 Use the limit definition of derivative \(f'(x) = \lim\limits_{h \to 0} \frac{f(x+h) - f(x)}{h}\) to compute \(f'(a)\) and find an equation of the tangent line. 1. \(f(t) = t - 2t^2, \quad a = 3\) 2. \(f(x) = \sqrt{x + 4}, \quad a = 1\) 3. \(f(x) = \frac{1}{\sqrt{x}}, \quad a = 4\)
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