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# f09e1s - 12 01 = x or x = 1200cc 10 Graph the function 3 2...

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Fall 2009 92.131 Exam 1 Solutions 92.131 Fall 2009 x −3 −2 −1 1 2 3 4 y −15 −10 −5 0 5 10 15 1) 2 / 1 2 / 5 2 1 2 3 ) ( + + = x e x x f x and so 2 / 3 2 / 7 4 1 4 15 ) ( + = x e x x f x 2) ) 3 ( 3 ) ( 2 3 2 t e t e t e t t g t t t + = + = . Horizontal tangents are where 0 ) ( = t g , so 0 , 3 = t . 3) x e x x f cos 2 ) ( = . 4) ) 1 sec 2 ( sec or ) sec (tan sec ) ( 2 2 2 + = t t t t t t s . 5) h x x h x h x h x f h x f x f h h + + = + = 1 3 1 ) ( 3 lim ) ( ) ( lim ) ( 2 2 0 0 2 2 0 0 0 0 0 2 0 2 2 2 0 6 1 6 ) ( 1 lim 6 ) ( lim 6 ) ( lim 6 lim 1 1 lim 3 6 lim 1 1 3 3 6 3 lim + = + = + + = + + = + + + = + + + = + + + + = x x x x h x x x h h x x h x h h x x x h x x h h x x h h h x h h x x x h h x x h h h h h h h Power rule is 1 = k k x k x dx d . 2 1 2 1 2 6 ) ( ) 3 ( ) 3 ( + = = x x x dx d x dx d x x dx d 6) 2 4 3 ) 3 ( 8 ) ( + = t t t g 7) x x x x x x f sin ) 4 2 ( cos ) 1 ( ) ( 2 2 + + = 8) Since 4 ) 1 ( = f , the point on the T.L. is ) 4 , 1 ( . Since 3 2 4 2 3 ) ( x x x f + + = the slope of the T.L. is 9 ) 1 ( = f . So ) 1 ( 9 4 = x y and so 5 9 = x y 9) a) ) 1000 ( 064 . ) 1000 ( 076 . 054 . 0 x x + = + or x x 064 . 0 64 76 054 . 0 + = + b) Equation can be reduced to
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Unformatted text preview: 12 01 . = x , or x = 1200cc 10 Graph the function 3 2 ) ( 2 + − = x x x f on the interval [ − 3, 4] below indicating scales, and labeling the vertex and all intercepts as well as end-points. Answer: Endpoints are in green ( − 3, − 12), and ( 4 , − 5). x- intercepts are ( − 1, ), and ( 3 , ). y-intercept is (0, 3) in red, and vertex in blue is (1, 4)....
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