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Get Full Access to Calculus: Early Transcendentals - 1 Edition - Chapter 3.1 - Problem 63ae
Get Full Access to Calculus: Early Transcendentals - 1 Edition - Chapter 3.1 - Problem 63ae

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Vertical tangent lines If a function f is continuous ata ISBN: 9780321570567 2

Solution for problem 63AE Chapter 3.1

Calculus: Early Transcendentals | 1st Edition

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Problem 63AE

Vertical tangent lines? ?If a function f is continuous at?a and , ?then th?e ?cur? ?y=? (?x) ?has a vertical tangent line at a and the equation of the tangent? line? is x =? . ?If a is an endpoint of a domain, then the appropriate one-sided derivative (Exercises 59-60) is used. Use this definition to answer the following questions. ? ? eri? that ? ? ) = ?x1/3 has a vertical tan?gent line at ? = 0.

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SOLUTION If a function f is continuous at a and lim|f (x)| = , then the curve y= f(x) has a xa vertical tangent line at a and the equation of the tangent line is x = a STEP 1 Given f(x) = x 3 1 11 1 2 Then f (x) = 3 3 = 3 3 STEP 2 Now let us take the left hand and the right hand limits. 1 2 lim+|f(x)| = lim + 3 |= x0 x0 1 32 lim|f(x)| = lim 3 |= x0 x0 Therefore,we have lim +f(x)| = lim f(x)| = x0 x0 Thus the given function has a vertical tangent line at x=0 STEP 3 The graph of the given function is

Step 2 of 3

Step 3 of 3

ISBN: 9780321570567

This full solution covers the following key subjects: vertical, Tangent, line, function, definition. This expansive textbook survival guide covers 85 chapters, and 5218 solutions. This textbook survival guide was created for the textbook: Calculus: Early Transcendentals, edition: 1. The full step-by-step solution to problem: 63AE from chapter: 3.1 was answered by , our top Calculus solution expert on 03/03/17, 03:45PM. Calculus: Early Transcendentals was written by and is associated to the ISBN: 9780321570567. Since the solution to 63AE from 3.1 chapter was answered, more than 402 students have viewed the full step-by-step answer. The answer to “Vertical tangent lines? ?If a function f is continuous at?a and , ?then th?e ?cur? ?y=? (?x) ?has a vertical tangent line at a and the equation of the tangent? line? is x =? . ?If a is an endpoint of a domain, then the appropriate one-sided derivative (Exercises 59-60) is used. Use this definition to answer the following questions. ? ? eri? that ? ? ) = ?x1/3 has a vertical tan?gent line at ? = 0.” is broken down into a number of easy to follow steps, and 78 words.

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