The limit lim x-> 0 e^x-1/x equals a derivative f' (c), for some function f(x) and some real number c. (i) find f(x) and c. (ii) Use the derivative of the function f(x) to evaluate the limit. (iii) Find an equaiton of the tangent line to y = f(x) at x = c, for the value of c you found in (i).

The limit lim x-> 0 e^x-1/x equals a derivative f' (c), for some function f(x) and some real number c. (i) find f(x) and c. (ii) Use the derivative of the function f(x) to evaluate the limit. (iii) Find an equaiton of the tangent line to y = f(x) at x = c, for the value of c you found in (i).

Calculus For The Life Sciences

2nd Edition

ISBN:9780321964038

Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.

Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.

Chapter3: The Derivative

Section3.5: Graphical Differentiation

Problem 2E

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Question

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The limit

lim x-> 0 e^x-1/x

equals a derivative f' (c), for some function f(x) and some real number c.

(i) find f(x) and c.

(ii) Use the derivative of the function f(x) to evaluate the limit.

(iii) Find an equaiton of the tangent line to y = f(x) at x = c, for the value of c you found in (i).

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