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43. Show that √(x) = {2²2 ²+ 2x, [x² +1, x ≤ 1 x > 1 is continuous and differentiable at x = 1. Sketch the graph of f.

43. Show that √(x) = {2²2 ²+ 2x, [x² +1, x ≤ 1 x > 1 is continuous and differentiable at x = 1. Sketch the graph of f.

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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mee hif- be me nd of b. ban of functions that are not differentiable, and explain the relationship between differentiability and continuity. 41. Show that f(x) = 3x is continuous at x = 0 but not dif- ferentiable at x = 0. Sketch the graph of f. 3 42. Show that f(x) = √(x - 2)² is continuous at x = 2 but not differentiable at x = 2. Sketch the graph of f.T.E 43. Show that f(x) = = x² +1, x ≤ 1 X 12.x, x > 1 is continuous and differentiable at x = 1. Sketch the graph of f. ^^ Show that
Transcribed Image Text:mee hif- be me nd of b. ban of functions that are not differentiable, and explain the relationship between differentiability and continuity. 41. Show that f(x) = 3x is continuous at x = 0 but not dif- ferentiable at x = 0. Sketch the graph of f. 3 42. Show that f(x) = √(x - 2)² is continuous at x = 2 but not differentiable at x = 2. Sketch the graph of f.T.E 43. Show that f(x) = = x² +1, x ≤ 1 X 12.x, x > 1 is continuous and differentiable at x = 1. Sketch the graph of f. ^^ Show that
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According to given data we can find the limit and derviative values in both side  And if  both side is equal it means this function is continuous and derviative.

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