Calc1 Final prep (1)

# Calc1 Final prep (1) - Final exam will cover from CHAPTER 3...

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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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