hwk2 - -√ 1-2 x x(d lim t → t t sin t 1(e lim z →∞...

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HOMEWORK ASSIGNMENT #2 due in class on Friday, September 20 Student No: Name (Print): Note: All homework assignments are due in class one week after being assigned. They must be on standard 8 1 2 × 11 size paper and they must be stapled. Assign- ments which are not stapled will not be accepted. I will not bring a stapler to class. Please enter your student number and name (as it appears on the regis- trar’s list) in the spaces above. SURNAME FIRST IN CAPITALS, and given name second. Please put your answers in the boxes (if provided) and submit these pages for your assignment. 1. Compute the following limits: (a) lim x 0 sin( - x ) sin 3 x (b) lim θ 0 θ 3 (sin θ ) 2 (c) lim x 0 1+2 x

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Unformatted text preview: -√ 1-2 x x (d) lim t → t t + sin t 1 (e) lim z →∞ z 2 + 1 2 z 2-1 (f) lim x →-∞ cos x x 2 + 1 2. Let f ( x ),-∞ < x < ∞ , be the function deﬁned as follows: f ( x ) = ( x + λ if x ≤ 2 2 λ-x if x > 2 (a) Determine the constant λ so that f ( x ) is continuous for all x . (b) Graph the function y = f ( x ),-4 ≤ x ≤ 8, for the value of λ found in (a). 2 3. Show that the function f ( t ) = cos t-t has a zero in the interval π/ 6 < t < π/ 4. 4. Using only the deﬁnition of the derivative, ﬁnd f ( x ) for the following functions: (a) f ( x ) = 1 √ x 2 + 1 (b) f ( x ) = x 1 + 2 x 3...
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This note was uploaded on 01/12/2010 for the course STAT 100 taught by Professor Denissjerve during the Winter '06 term at San Jose State.

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hwk2 - -√ 1-2 x x(d lim t → t t sin t 1(e lim z →∞...

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