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PracticeExam1

# PracticeExam1 - f has a removable discontinuity at x = 3...

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MATH 191, Sections 1 and 3 Calculus I Fall 2007 Practice Exam 1 This practice exam, like the actual exam will be, is worth a total of 100 points, and point values for each question are given below. It is similar in length, format, and tested content to the actual exam, but in the interest in saving paper I have omitted space for you to work your solutions; you should work these out on your own paper. Answer every question fully and clearly. Please show your work where appropriate, and circle or box your final answer. Please let me know if you have any questions! 1. (15 points) Find numbers C and a such that the exponential function f ( x ) = Ca x satisfies f (1) = 2 and f (3) = 18. 2. (15 points) On a set of axes of your own, draw a graph of a single function f satisfying the following conditions: (a) lim x →- 2 - f ( x ) = lim x →- 2 + f ( x ), (b) lim x 0 f ( x ) =
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Unformatted text preview: f has a removable discontinuity at x = 3. 3. (10 points) Explain brieﬂy (and demonstrate!) how to graph the function H ( x ) = 2 | x-1 | -3 without a calculator. 4. (20 points total) (a) (6 points) Explain brieﬂy why you cannot use direct substitution to ﬁnd the limit lim x → 2 x 2 + x-6 x 2-4 . (b) (7 points) Find the limit in (a). (c) (7 points) Is the function x 2 + x-6 x 2-4 continuous at the point x = 2? Explain your answer brieﬂy. 5. (12 points) Find the inverse of the following function, and state the domains of both the function and the inverse: f ( x ) = 4 ln ( x 5-2 ) . 6. (28 points total; 7 points each) Compute the indicated limits. (a) lim x → 1 x 2 (b) lim t → π/ 2 cos( t ) (c) lim r →-∞ e r (d) lim x → √ x-2 x-4...
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