Answered: THEOREM 11.5.2 THE CAUCHY MEAN-VALUE… | bartleby

Algebra & Trigonometry with Analytic Geometry

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter6: The Trigonometric Functions

Section6.6: Additional Trigonometric Graphs

Problem 78E

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Practice using 11.5.2 to derive 11.6.1

THEOREM 11.5.2 THE CAUCHY MEAN-VALUE THEOREM*
Suppose that f and g are differentiable on (a, b) and continuous on [a, b]. If
g is never 0 in (a, b), then there is a number rin (a, b) for which
f'(r) f(b) - f(a)
g'(r)
=
g(b)g(a)

(11.6.1)
L'HÔPITAL'S RULE (00/00)
Suppose that
f(x) → ±0
and
g(x)
→ ±8
and in the approach g(x) 0.
f'(x)
f(x)
If
→Y,
then
→ Y.
g'(x)
g(x)

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