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# HW1 - x 2 6 x-7 x 3-x 2 2 x-2 Problem 5(5 points Compute...

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MATH 102, ASSIGNMENT 1 DUE MAY 19 Problem 1. (2 points) Give an example of a function f ( x ) satisfying the indicated properties, or explain why such a function cannot exist: a) lim x 5 f ( x ) = 3, but lim x 5 - f ( x ) does not exist b) lim x 5 - f ( x ) = 3, but lim x 5 f ( x ) does not exist Problem 2. (3 points) Sketch the function y = x 2 - 6 x + 9 x - 3 Specify its domain and its range. Find the vertical and horizontal asymptotes (if any). Problem 3. (5 points) a) Compute the following limit: lim Δ x 0 + ( x + Δ x ) 3 - x 3 Δ x b) Which integers n have the property that lim x + x n = 1 ? Problem 4. (5 points) Compute the following limits: lim x 0 x 2 + 6 x - 7 x 3 - x 2 + 2 x - 2 , lim x 1 x 2 + 6 x - 7 x 3 - x 2 + 2 x - 2
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Unformatted text preview: x 2 + 6 x-7 x 3-x 2 + 2 x-2 Problem 5. (5 points) Compute the following limits: lim x → √ x + 4-2 x , lim x → 5 √ x + 4-2 x , lim x → ∞ √ x + 4-2 x Problem 6. (5 points) Find the asymptotes (vertical and horizontal, if any) for the following functions: a) x √ 1-x 2 b) x + p 1 + x 2 J-RULE: Just answers - “yes”, “5” - won’t get you full marks, but (correctly) justiﬁed answers - “yes, because. ..”, “(some algebra). .. (sweat sweat) . .. (swear swear) . .. 5” - will. 1...
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