practice-problems - University of Engineering and...

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Unformatted text preview: University of Engineering and Technology Lahore Department of Electrical Engineering Midterm Practice Problems Calculus I January 5, 2010 Total marks: 30 Time 90 mins Instructions • Give brief and concise answers. Do not needlessly fill pages. 1. Compute lim x →∞ 1 x + 1 ln x using the Sandwich theorem and other limit the- orems. 2. Let F ( x ) = x 2- 1 | x- 1 | . Find (a) lim x → 1 + F ( x ) (b) lim x → 1- F ( x ). Does the limit lim x → 1 F ( x ) exist? 3. If lim x → a [ f + g ] ( x ) = 2 and lim x → a [ f- g ] ( x ) = 1, what is lim x → a [ fg ] ( x )? 4. Show that when p > 0, lim x →∞ ln x x p = 0 5. Find a point on the parabola y = 2 x 2 that is closest to the point (1 , 4) . 6. Consider the function w defined by w ( x ) = f ( g ( h ( x ))) + k ( x ) where f , g , h and k are functions which are differentiable everywhere on the real line. Compute w ( x ). 7. Compute the limit (Hint: Write d dx e x as a limit) lim x → 1 e x- e x 2- 1 8. Construct a function f...
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This note was uploaded on 01/10/2011 for the course EE 100 taught by Professor Razasuleman during the Spring '10 term at University of Engineering & Technology.

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practice-problems - University of Engineering and...

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