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Day04-1432class

# Day04-1432class - ln = 2 x y e at the point 29 2 4 29 2 5x...

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Math 1432 Section 23986 Pam Balthazar [email protected] 620 PGH Office Hours in 222 Garrison (CASA): Today 1 – 3:00 Homepage www.math.uh.edu/~pamb and click on Calculus 1432 READ YOUR BOOK!!!

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Poppers will be given in class starting next week. Make sure you have a package of the bubbling forms from the Copy Center. Reminder: Take the online quizzes.
Section 7.3/7.4 Quick Review. . . x 1 1 x dt x 0 t ln = d 1 x x 0 dx x ln = d u u dx u ' ln = u a positive function of x dx x C x 0 x ln , = + ( 29 ( 29 ( 29 ( 29 g x g x C g x 0 g x ' ln , = +

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( 29 x x f ln = ( 29 1 x x e f - = ( 29 ( 29 1 x x f f - = ( 29 ( 29 1 x x f f - = ( 29 ( 29 x x e e x f ln = = ( 29 1 x x e x ln f ln - = =

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, u is a function of x Examples: 3x d e dx = And, x x e dx e C = + u u e du e C = + 5 x 5e dx = ( 29 ( 29 x x d d x e x e dx dx exp exp = = = ( 29 ( 29 u u d du u u dx dx d du e e dx dx exp exp = =
y’ = ( 29 ( 29 ( 29 x 2x f sin ln = ( 29 x f ' = 3 x e dx x e dx ln x x e y 1 e ln = +

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x y e 4x ln = + 2 2x x y x e e x ln = -
Find the equation of the tangent line to at the point (1, 1). 1 x y e - =

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Find the equation of the normal line to

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Unformatted text preview: ln = 2 x y e at the point . ( 29 2 4 ,-( 29 2 5x x dx exp-âˆ« 1 x 2 e dx x âˆ« Section 7.5 Arbitrary Powers; Other Bases Find the derivative of an exponential function with base a x y a = u y a = Find the derivative of a log function with base a. Use change of base. a y x log = a y u log = Find the derivative of each. x y 2 = 2 3 x y 5 = ( 29 y x log cos = ( 29 x y 2 ln cos = ( 29 5 y x log tan = 2 2 x y x 1 log = - ( 29 3 x y x 7-= ( 29 x y 1 x = + Examples: x x 1 a dx a c a ln = + âˆ« u u 1 a du a c a ln = + âˆ«-= âˆ« x 4 dx x 3 dx = âˆ« ( 29 2 x x 5 dx = âˆ« Find the area bounded by , y = 0 1 x 2 x e 1 y x 1 , , = = + =-...
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