Unformatted text preview: Final exam will cover from CHAPTER 3 to CHAPTER 5 section 4.
1 #1 Differentiate ( ) = 3 + −4/3 .
−3 7 4 ′ () = 4 − 3 −3
#2 Find the derivative of the polynomial function
( ) = 3 4 + 2 3 + 11 + 912 . ′ ( ) = 12 3 + 6 2 + 11
( −1)( 2 −3 ) #3 Find the derivative of ( ) =
.
2
3
′( ) = 1 − 2 #4 Find the derivative of ( ) = 2 + .
′( ) = 2 + #5 Find the derivative of ( ) = 5 + sin +
cos .
′( ) = 5 4 + cos − sin .
cos #6 Differentiate ( ) = sin . 1 1
= ln 9
#18 Calculate the tangent line equation to the ellipse
given by 2 + 2 + = 4 at (1,2). = − + 3
#19 Find the absolute maximum and minimum
values of ( ) = 3 − 3 on the interval [0, 2]. Abs
max = 2 at x = 2, abs min = 2 at x = 2
4 #20 Find the absolute maximum and minimum
values of f()=(2−ln) on the interval [1, 2 ]. Abs
max = e at x = e, abs min = 0 at x = e2 .
#21 Find the coordinates of any critical points of
1
1
( ) = 3 3 − 2 2 − 2 + 11. x = 2, or 1 −1 ′( ) = sin2 .
#7. Differentiate ( ) = 2 cos ′ () = 2 cos − 2 sin #8. Differentiate ( ) = 3 cos ′ () = 3 2 cos − 3 sin cos #9. Differentiate ( ) = cos( 4 + sin ) ′ ( ) = −(4 3 + cos ) sin( 4 + sin )
#10. Differentiate ( ) = ln( + − ) − − ′ ( ) = + − #11 Find 3 + 3 = 12. 2
=− 2 2
#12 Find
for ( ) = 2 sin + 3 4. = 4 sin + 2 2 cos + 12 3 2 3 +3
#13 Find the derivative of ( ) = 5 2 +4.
4 2 10 +24 −30
′( ) =
( 5 2 +4) 2 #14 Calculate the tangent line equation of ( ) =
2 at = 1 = 4 − 2
#15 Calculate the tangent line equation of ( ) =
1
2√ at = 4. = + 2 #22 Find the coordinates of any critical points of
( ) = − . x = 1
#23 Find all local max or min of () = (3 − 2 ) .
1 #24 Find all local max or min of () = 3 − 2 −
3
3 + 1.
#25 Find all local max or min of () = − .
#26 Find all local max or min of () = 4 − 2 3 + 1
#27 Calculate the limit lim
→0 #28 Calculate the limit lim
→0 2−sin 2
3
2 −1+
2 . . #29 Calculate the indefinite integral
∫ 3 −2
2 √ . #30 Calculate the indefinite integral
∫ 7 + cos 3 + sin 2 . 2 #16 Calculate the tangent line equation to ( ) = cos sin at = 0.
= +1 #17 Find for =ln( ln(9) ). #31 Calculate the indefinite integral
1
1
∫ 2 + 22 . Final exam will cover from CHAPTER 3 to CHAPTER 5 section 4.
#32 Calculate the Riemann sum of
1 ≥ 0 ( ) = {
on [−2, 2]
−2 < 0
using the partition = { −2, −1.6, −1.2, −0.8, −0.4, 0, 0.4, … ,1.6, 2} and the center points in each subinterval.
#33 Calculate the Riemann sum of
( ) = 2 on [0, 10]
using the partition = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10} and the center points in each subinterval. #34 ( ) = ∫1 1
2 +2 . Calculate ′( ). #35 ( ) = ∫0 sin 2 . Calculate ′( ).
4 #36 Calculate ∫2 3 2 #37 Calculate ∫−2 4 − 4 2 21 #38 Calculate ∫1 − 1
2 /4 #39 Calculate ∫−/4 sin 4 − cos 2 #40 (True or False) If a function has positive
function values on [a, b], then the function is
integrable on [a, b].
#41 (True or False) If ′ ( ) = (), then ∫ () = () − () + , where C is a
random constant. #42 (True or False) If ( ) = ∫−1 (),
1 ≥ 0
where () = {
, then ( ) is
−1 < 0
differentiable and ′( ) = (). ...
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 Fall '09
 MARTHAROYER
 Calculus, Derivative, Sin, Tangent line equation, Riemann, Calculate

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