MATH 220 Midterm: MATH 220 KSU Test 1s08
15 Feb 2019
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Please write legibly and organize your solutions in a logical and coherent form; answers which are illegible or confusing will not receive credit. You may not use notes, books or calculators. The point value of each problem is listed next to the problem number. (20 pts. ) Find each limit. (a) lim x 5 x2 4x 5 x 5 (b) lim x 0. 1 x + 1 x (c) lim t 1 t3 + + x (a) use the de nition of derivative as a limit to compute f (x). (b) find the equation of the tangent line to the curve y = f (x) at the point where x = 1. (10 pts. ) Show that the equation x5 x2 2 = 0 has at least one root inside the interval 0 x 2. (10 pts. ) Show that there is a number a > 0, such that the equation 2x the interval (a, 1).
