CalIEx1Spring2002 - using the definition . 2 1 ) ( = x x f...

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Calculus I Exam #1 Spring 2002 Name ___________________________ You must show your work. All answers must be exact unless indicated otherwise. 1. Use the given graph of to find the limits. (3 points each) ) ( x f y = x y -6 -4 -2 0 2 4 6 -2 0 2 a. = __________ b. = __________ c. = __________ ) ( lim 2 x f x + ) ( lim 1 x f x ) ( lim 0 x f x 2. Evaluate the limit analytically. (7 points each) a. = _____________ b. x e x x 2 cos lim 3 0 x x x 3 3 0 + lim = __________________ c. θ sec 1 sec lim 0 = ______________ 3. Given that is continuous at x = 5, what three things do we know must be true about ? ) ( x f y = f (6 points)
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4. Find the derivative of the function. Do not simplify your answers. (6 points each) a. b . ( f = ) 7 5 ln( 3 ) ( 4 = x x x f () 2 8 3 arctan ) 3 x e x x + 5.
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Unformatted text preview: using the definition . 2 1 ) ( = x x f (10 points) 6. Find the equation of the tangent line of the function when . You may leave your answer in point-slope form. (7 points) x e y 2 4 = 1 = x 7. Find the derivative of the function. Do not simplify your answers. (7 points each) a. 3 5 sec ) ( 2 + = x x x x f b. x y = x cot 3 c. ) 4 sin(cos ) ( x x f = 8. Find dx dy . Circle your answers. (7 points each) a. 5 sin 3 2 2 = + y x y x b. 1 + = x x y BONUS Find functions and such that lim and but lim . f g = ) ( x f c x = ) ( lim x g c x [ ] ) ( ) ( x g x f c x...
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This note was uploaded on 01/12/2012 for the course MATH 2554 taught by Professor Pamelasatterfield during the Spring '11 term at NorthWest Arkansas Community College.

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CalIEx1Spring2002 - using the definition . 2 1 ) ( = x x f...

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