> Graph the function f(x) = V1– x² ,0

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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HomeWorkS
> Graph the function f (x) = v1– x² , 0< x <1 and then find the inverse of the function>
• If f(x) = x* Identify the domain and range of the inverse function.
1
> If f(x) =x + 7, estimate the derivative of the inverse function at (x-f(a)) and (a=-1)
KIRKUK UNIVERSITY
5
> If f(x)
= x³ & g(x) = x
a) Show that g(x) is inverse of f(x) b) Find the tangent slope for f(x) & g(x) at (1,1) and (-1,-1)
c) What lines are tangent to the curves at the origin?
> Express In 0.75 in terms of In 2 and In 3
In(3x? – 9x) + In
1
Use the properties of logarithms to simplify the expression
If
y = In(In(In x)),
find dy/dx
> If
y = In(sec 0 + tan 0),
find dy/dx
4 sin e
原:
Evaluate
1-4 cos 0
If y = (x2 + 1)(x– 1)2 , use logarithmic differentiation to find the derivative of y with
respect to the given independent variable.
Reference: Thomas Calculus, 13th Edition by George B. Thomas.
2005-1420
Transcribed Image Text:HomeWorkS > Graph the function f (x) = v1– x² , 0< x <1 and then find the inverse of the function> • If f(x) = x* Identify the domain and range of the inverse function. 1 > If f(x) =x + 7, estimate the derivative of the inverse function at (x-f(a)) and (a=-1) KIRKUK UNIVERSITY 5 > If f(x) = x³ & g(x) = x a) Show that g(x) is inverse of f(x) b) Find the tangent slope for f(x) & g(x) at (1,1) and (-1,-1) c) What lines are tangent to the curves at the origin? > Express In 0.75 in terms of In 2 and In 3 In(3x? – 9x) + In 1 Use the properties of logarithms to simplify the expression If y = In(In(In x)), find dy/dx > If y = In(sec 0 + tan 0), find dy/dx 4 sin e 原: Evaluate 1-4 cos 0 If y = (x2 + 1)(x– 1)2 , use logarithmic differentiation to find the derivative of y with respect to the given independent variable. Reference: Thomas Calculus, 13th Edition by George B. Thomas. 2005-1420
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