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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- Fall '07
- Calculus, Continuous function, x2 lim cos, lim er x-2