A "zoom" on the graph of y = f(x) near (xo, Yo) (with yo = f(xo)) with magnification factor M (the same in both r and y directions) is the graph of the function defined by f(ro + x/M) = yo + y/M. Prove that if f is differentiable at x0, then the zoom converges to the straight line through the origin with slope f'(xo), as M → o. What happens to the zoom of Jx| near the origin?

A "zoom" on the graph of y = f(x) near (xo, Yo) (with yo = f(xo)) with magnification factor M (the same in both r and y directions) is the graph of the function defined by f(ro + x/M) = yo + y/M. Prove that if f is differentiable at x0, then the zoom converges to the straight line through the origin with slope f'(xo), as M → o. What happens to the zoom of Jx| near the origin?

College Algebra (MindTap Course List)

12th Edition

ISBN:9781305652231

Author:R. David Gustafson, Jeff Hughes

Publisher:R. David Gustafson, Jeff Hughes

Chapter3: Functions

Section3.3: More On Functions; Piecewise-defined Functions

Problem 99E: Determine if the statemment is true or false. If the statement is false, then correct it and make it...

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