Fall2009

# Fall2009 - MATH 1241 FINAL EXAM FALL 2009 PART...

This preview shows pages 1–5. Sign up to view the full content.

MATH 1241 FINAL EXAM FALL 2009 PART I (Calculators not allowed) 1. Which of the following does not represent the deﬁnition of the derivative of f ( x )? (a) lim h 0 f ( x + h ) - f ( x ) h (b) lim x a f ( x ) - f ( a ) x - a (c) lim 4 x 0 f ( x + 4 x ) - f ( x ) 4 x (d) lim 4 x 0 4 y 4 x (e) None of the above. 2. Compute d dx ± 2 e x - 7 x + 3 ln x ² (a) 2 e x + 7 x 2 + 3 x (b) 2 e x - 7 x 2 + 3 x (c) 2 e x + 7 x 2 - 3 x (d) 2 e 0 + 7 1 + 3 ln 1 (e) 2 e x - 7 + 3 x 3. Compute d dx [ x 2 tan x ] (a) 2 x sec 2 x (b) 2 x + sec 2 x (c) x 2 sec 2 x + 2 x tan x (d) x 2 sec 2 x - 2 x tan x (e) 2 x tan x - x 2 sec 2 x 1

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
MATH 1241 FINAL EXAM Fall 2009 4. Compute d dx ± x sin x e x ² (a) x (cos x + sin x ) - sin x e x (b) x (cos x - sin x ) + sin x e x (c) x (cos x + sin x ) + sin x e x (d) x (sin x - cos x ) - sin x e x (e) x cos x + sin x e x 5. Compute d dx ³ sin ( x 3 ) - sin 3 ( x ) ´ (a) 3 sin 2 ( x ) cos ( x ) - 3 x 2 cos ( x 3 ) (b) sin (3 x 2 ) - 3 sin 2 ( x ) (c) cos ( x 3 ) - 3 sin 2 ( x ) (d) 3 x 2 cos ( x 3 ) - 3 sin 2 ( x ) cos ( x ) (e) 0 6. Compute d dx [ln (ln ( x ))] (a) 1 ln ( x ) · 1 x (b) x ln ( x ) (c) 1 ln ( x ) (d) ln µ 1 x (e) ln µ 1 x + 1 x ln x 2
MATH 1241 FINAL EXAM Fall 2009 7. Compute d dx h sin x i (a) 1 2 sin x (b) cos x (c) cos x 2 sin x (d) 1 2 cos x (e) 1 2 sin x cos x 8. Find the value of h 0 (2) where h ( x ) = x 2 f ( x ) , f (2) = 3 and f 0 (2) = - 2 . (a) - 4 (b) - 8 (c) - 20 (d) 4 (e) 20 9. Find the value of ( g h ) 0 (2) from the values in the following table. Here ( g h ) ( x ) = g ( h ( x )) and ( g h ) 0 (2) is the derivative of this composition evaluated at x = 2 . x g ( x ) h ( x ) g 0 ( x ) h 0 ( x ) 1 - 1 4 10 3 2 0 3 1 - 4 3 2 7 5 2 (a) 1 (b) - 4 (c) 3 (d) 0 (e) - 20 3

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
MATH 1241 FINAL EXAM Fall 2009 10. At which point(s) ( x =?) is the slope of the tangent line to the graph of
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

### Page1 / 14

Fall2009 - MATH 1241 FINAL EXAM FALL 2009 PART...

This preview shows document pages 1 - 5. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online