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# quiz3 - ± x-1 x 2-1 if ≤ x< 1 a cos πx if x ≥ 1...

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MATH 151: Calculus I Quiz 3 Name: Section: This is a 30 minute quiz. Please write your answers clearly and explain your thinking carefully. No books or notes may be used. You are not allowed to use a calculator during this quiz. This quiz is worth 30 points. Question Score 1 /8 2 /6 3 /8 4 /8 Total /30 1. Compute the following limits. (a) lim x 0 x + 9 - 3 x (b) lim x 0 tan x x

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MATH 151:Calculus I Quiz 3 (c) lim x 0 sin px x , where p is a constant. (d) lim x 0 sin px sin qx , where p and q are constants and q 6 = 0. 2. Let the function f : [0 , ) 7→ R be given by f ( x ) =
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Unformatted text preview: ± x-1 x 2-1 if ≤ x < 1 a cos( πx ) if x ≥ 1 Choose a such that f is continuous at x = 1. 3. (a) State the Squeeze Theorem. MATH 151:Calculus I Quiz 3 (b) Show that lim x → + √ x cos 2 ± 1 x ² = 0 . 4. (a) State the Intermediate Value Theorem. (b) Show that f ( x ) below has a zero in the given interval. That is show, there is at least one c in the given interval such that f ( c ) = 0. f ( x ) =-x 3 + 4 x + 2 , [-1 , 1]...
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quiz3 - ± x-1 x 2-1 if ≤ x< 1 a cos πx if x ≥ 1...

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