{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

2004 Fall - 125FinalFall04short math125

# 2004 Fall - 125FinalFall04short math125 - MATH 125 FINAL...

This preview shows pages 1–3. Sign up to view the full content.

MATH 125 FINAL EXAM (common exam) December 2004 1. (5 points each) Compute the following limits, if they exist. You may not use l’Hˆ opital’s rule, if you know what that is. You must also justify your answer. (a) lim x + 3 x 2 + 1 (1 - x )(2 x - 1) (b) lim x 0 x cot 7 x (c) lim x 1 5 - x - 4 x x 2 - 1 2. (6 points each) Find dy dx of the following functions. (You do not need to simplify your answer.) (a) y = sin ( ln(1 + x 100 ) ) (b) y = x e e x (c) y = x 0 (1 + e - t 2 ) dt (d) y = tan x 1 + sec x 3. (6 points each) Evaluate the following integrals. (You do not need to simplify your answer.) (a) 5 x 2 + 1 x + 2 cos 2 x - sin x dx (b) 1 0 x cos(1 + x 2 ) dx (c) 5 x 1 + 5 x dx 4. (12 points) Knowing that 4 81 = 3, use a linear approximation to estimate 4 85. 5. (15 points) Find an equation of the tangent line to the curve xe 2 x - y 2 ln y = 0 at the point (1 , e ). 6. (7 points each) Consider the function f ( x ) = x cos 1 x if x = 0 0 if x = 0 (a) Is f continuous at x = 0? Explain your answer. 1

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

View Full Document
(b) Is f differentiable at x = 0? Explain your answer.
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}