1. As an ordered pair, find the point at which the tangent line to f(x)= arcsin(x)arccos(x) at x=0 intersects the horizontal tangent line of f(x)

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.
Chapter6: Applications Of The Derivative
Section6.CR: Chapter 6 Review
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1. As an ordered pair, find the
point at which the tangent line to
f(x)= arcsin(x)arccos(x) at x=0
intersects the horizontal tangent
line of f(x).
2. The length of a curve f(x) on the
interval [a,b] can be found by
integral sqrt(1 + f'(x)^2) dx. Show
that hyperbolic cosine function
has the "neat" feature in which the
area under it over an interval [a,b]
is the same as the length of the
curve over this interval.
Transcribed Image Text:1. As an ordered pair, find the point at which the tangent line to f(x)= arcsin(x)arccos(x) at x=0 intersects the horizontal tangent line of f(x). 2. The length of a curve f(x) on the interval [a,b] can be found by integral sqrt(1 + f'(x)^2) dx. Show that hyperbolic cosine function has the "neat" feature in which the area under it over an interval [a,b] is the same as the length of the curve over this interval.
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