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22. Use graphs to discover the asymptotes of the curve. Then prove what you have discovered.

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17. Find the limit. lim(x→∞)⁡(√(x^2+4x+1)-x)

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11. Find the limit. lim(u→1)(u^4-1)/(u^3+5u^2-6u)

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9. Find the limit. lim(r→9)⁡√r/(r-9)^4

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26. If |f| is continuous at a, so is f. Determine whether the statement is true or false. If it is

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2. lim(x→1)⁡(x^2+6x-7)/(x^2+5x+6)=lim(x→1)⁡(x^2+6x-7)/lim(x→1)⁡(x^2+5x+6) Determine whether the

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16. Describe several ways in which a function can fail to be differentiable. Illustrate with

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8. (a) Give examples of functions that are continuous on [-1,1]. (b) Give an example of a function

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6. Which of the following curves have vertical asymptotes? Which have horizontal asymptotes? (a) y=x

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2. Describe several ways in which a limit can fail to exist. Illustrate with sketches.

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1. Explain what each of the following means and illustrate with a sketch. (a) lim(x→a)⁡f(x)=L (b)

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65. Nick starts jogging and runs faster and faster for 3 minutes, then he walks for 5 minutes. He

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62. (a) Sketch the graph of the function g(x)=x+|x|. (b) For what values of x is g differentiable?

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61. (a) Sketch the graph of the function f(x)=x|x|. (b) For what values of x is f differentiable?

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59. Show that the function f(x)=|x-6| is not differentiable at 6. Find a formula for f' and sketch

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57. Let f(x)=∛x.(a) If a≠0, use Equation 2.7.5 to find f'(a). (b) Show that f'(0) does not exist.

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56. (a) The graph of a position function of a car is shown, where s is measured in feet and t in

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55. If f(x)=2x^2-x^3, find f^' (x),f^'' (x),f^''' (x), and f^((4) ) (x). Graph f, f', f'', and f'''

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53. Use the definition of a derivative to find f'(x) and f''(x). Then graph f, f', and f'' on a

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51. The figure shows the graphs of three functions. One is the position function of a car, one is

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50. The figure shows graphs of f, f', f'', f''''. Identify each curve, and explain your choices.

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47. The graphs of a function f and its derivative f' are shown. Which is bigger, f'(-1) or f^'(1)?

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46. Zoom in toward the points (1,0),(0,1) and (-1,0) on the graph of the function g(x)=(x^2-1)^(2/3)

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45. Graph the function f(x)=x+√(|x| ). Zoom in repeatedly, first toward the point (-1,0) and then