Testing for Tangents35. Does the graph ofSx² sin (1/x), x # 0lo,f(x) =x = 0have a tangent at the origin? Give reasons for your answer.36. Does the graph ofSxsin (1/x), x+ 0lo,g(x) =x = 0have a tangent at the origin? Give reasons for your answer.Vertical TangentsWe say that a continuous curve y = f(x) has a vertical tangent at thepoint where x = xo if the limit of the difference quotient is o or -0o.For example, y = x/3 has a vertical tangent at x = 0 (see accompa-nying figure):f(0 + h) -limf(0)h/3= lim1= limh0h2/3= 00.yy = f(x) = x'/3VERTICAL TANGENT AT ORIGINHowever, y = x2/3 has no vertical tangent at x = 0 (see next figure):g(0 + h) - g(0)lim2/3= lim- 0h1= limh0 h/3

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Description: Testing for Tangents35. Does the graph ofSx² sin (1/x), x # 0lo,f(x) =x = 0have a tangent at the origin? Give reasons for your answer.36. Does the graph ofSxsin (1/x), x+ 0lo,g(x) =x = 0have a tangent at the origin? Give reasons for your answer.Vert

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Does the graph of Sx² sin (1/x), x # 0 lo, f(x) = x = 0 have a tangent at the origin? Give reasons for your answer.

Functions and Change: A Modeling Approach to College Algebra (MindTap Course List)

6th Edition

ISBN:9781337111348

Author:Bruce Crauder, Benny Evans, Alan Noell

Publisher:Bruce Crauder, Benny Evans, Alan Noell

Chapter1: Functions

Section1.2: Functions Given By Tables

Problem 32SBE: Does a Limiting Value Occur? A rocket ship is flying away from Earth at a constant velocity, and it...

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