practicetest1 - 9 A right cylinder is inscribed in a sphere...

Practice problems
1. Sketch the graph of the derivative of the following functions:
(page 142, problems 5-8)
2. Use Newton’s method to find the third approximation of a solution of
x
3
+ 2 x - 4 = 0 , if x
1
= 1 .
(page 298, problem 5)
3. Approximate 3
√
30 to eight decimal places. (page 298, problem 11)
4. Calculate by definition the derivative of g ( x ) =
1
x 2
. (page 144, problem 28)
5. Find equations of both lines through (2 , - 3) tangent to the parabola y = x + x
2
.(page 156, problem
72)
6. Differentiate
f ( x ) =
sin x
csc 2 x
.
7. Differentiate:
f ( x ) =
sec x
1 + sec x
.
(page 174, problem 11)
8. Differentiate:
( a ) f ( x ) = sin( 1 + x 2 ) , ( b ) f ( x ) = sin(tan
√
sin x ) .
(page 182, problems 31 and 41)