3rd - number c such that c 2 = 2 8 Find an equation of the...

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Math120 Recitation 3 October 4, 2006 1. Let f ( x ) = ± 4 - x 2 if x 2, x - 1 if x > 2. (a) Find lim x 2 - f ( x ) and lim x 2 + f ( x ). (b) Does lim x 2 f ( x ) exists? (c) Sketch the graph of f . 2. Show by means of an example that lim x a f ( x ) g ( x ) may exists even though neither lim x a f ( x ) nor lim x a g ( x ) exists. 3. Prove lim x →- 2 x 2 + 3 = 2 using ±, δ definition of limit. 4. Prove lim x 3 x 2 + x - 4 = 8 using ±, δ definition of limit. 5. Prove lim x →- 3 1 ( x +3) 4 = using definition of infinite limit. 6. Find the constant c that makes f continuous on ( -∞ , ). where f ( x ) = ± x 2 - c 2 if x < 4, cx + 20 if x 4. 7. Use the Intermediate Value Theorem to prove that there is a positive
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Unformatted text preview: number c such that c 2 = 2. 8. Find an equation of the tangent line to the curve y = √ 2 x + 1 at the point (4 , 3). 9. Find the derivative of the function f ( x ) = x + √ x by using the definition of derivative. Also state the domain of the function and derivative. 10. Where the function f ( x ) = b x c is not differentiable? Find a formula for f ( x ) and sketch its graph. 1...
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This note was uploaded on 04/30/2010 for the course MATHEMATIC MATH 119 taught by Professor Tor during the Spring '10 term at Middle East Technical University.

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