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4. (26 pts) Evaluate the limit or say that the limit does not exist . If a limit does not exist, explain why. Show your work. You may NOT use a table of values, a graph, or L' Hospitals's Rule to justify your answer. (Note: Possible answers include + or -.) X-2 (a) (10 pts) lim – x+2 782 +5 - 3 (b) (8 pts) xvot COS X OSCILLATES lim x → x + 4 x2 Since -1 scos x si, we have that -1 (c) (8 pts) cos x x + 4 x2 1 x + 4 x? x + 4 x2 -1 1 and since lim – Elim- x+ x + 4 x2 + x + 4 x2 * +422=0, it follows by the Squeeze Theorem that lim Co2 = 0. X +0 x + 4 x 2
1 10. Letf(x) = x² +3 --- 1. Its derivative satisfies 1 2.03 + x2 +1 (x + 1)(2.2 - 2+1) f'(x) = 2x +1+ = 22 (a) Evaluate lim f(c) and lim f(). 100- 20+
x + 4x +4 C. Evaluate ale lim + - x2-4 Your answer should be a number, + ,- , or DNE if the limit does not exist.
