plugin-thq1 - Differential Calculus Fall 2010 Take-Home...

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Unformatted text preview: Differential Calculus Fall 2010 Take-Home Quiz 1 1. Find the domain and range of the function 1) y = x2 + 1 2) y = - x - 2 3) y = 1 x+2 2. Evaluate the function as indicated. Determine its domain and range. f (x) = f (-2), 3x + 3, -x2 - 3, f (3), x<1 x1 f (t2 + 5) Find the composite functions (f g) and (gf ). What is the domain of each composite function? 3. f (x) = x2 + 1, 4. f (x) = x2 + 3, g(x) = sin x g(x) = 1 x-2 5. Find the limit L. Then use the - definition to prove that the limit is L. x2 lim (2x - 3) 6. Find the limit. 1) lim (2x3 - x + 5) x2 2) lim x+4 x2 x2 + 1 3) lim cos x x-2 7. Use the information to evaluate the limits xc lim f (x) = -3, xc lim g(x) = 5 1) xc 2f (x) + lim g(x) 2) lim 3f (x) g(x) xc Find the limit (if it exists). 8. lim 9. lim x2 - x - 2 x-1 x2 - 1 x2 - 9 x3 x2 - 5x + 6 10. Find the limit (if it exists). x1 x+3-2 x2 - 1 Determine the limit of the trigonometric function (if it exists) lim 11. lim sin 2x x0 3x tan2 x x0 2x 12. lim 13. lim 3(1 - cos x)2 x0 x f (x + x) - f (x) x0 x Find lim 14. f (x) = x + 1 15. f (x) = 2x2 - 1 Use the Squeeze Theorem to find lim f (x) x0 16. f (x) = x2 sin 3 x 17. 2 - 3x2 f (x) 2 + 5x2 Find the limit (if it exists) 18. lim + x4 |x - 4| x-4 f (x) = 2x2 + 2x + 1, x 0 x - 3, x>0 19. lim f (x), + x0 20. Find the limit (if it exists) lim f (x), f (x) = 10 - x, x 2 x2 + 2x, x > 2 x2 21. Solve the inequality 3x + 2 2x - 1 > x+3 2x + 1 ...
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This note was uploaded on 05/15/2011 for the course HIST 101 taught by Professor Mr.beckler during the Spring '11 term at Alabama State University.

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plugin-thq1 - Differential Calculus Fall 2010 Take-Home...

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