Barrons AP Calculus

(Marvins-Underground-K-12) #1
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If  sin (xy)    =   y,  then        equals
sec (xy)
y cos (xy) − 1

cos (xy)

Let x   >   0.  Suppose     and  ;  then    
f(x^4 )
f(x^2 )
2 xg (x^2 )

2 g(x^2 )   +   4x^2 f(x)

The region  bounded by  y   =   ex, y   =   1,  and x   =   2   is  rotated about   the x-axis.
The volume of the solid generated is given by the integral

Suppose the function    f   is  continuous  on  1    x  2,  that    f   ′(x)    exists  on  1   <
x < 2, that f(1) = 3, and that f(2) = 0. Which of the following statements is
not necessarily true?
The Mean-Value Theorem applies to f on 1 x 2.
exists.
There exists a number c in the closed interval [1, 2] such that f ′(c) =
0.
If k is any number between 0 and 3, there is a number c between 1
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