MATH116 Lecture Notes - Lecture 19: Opata Language
9 Dec 2015
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Tutorial problems 4: find the limit lim x . 9x6 x x3 + 1: make a careful sketch of the graph of y = f (x) = ln(x), and below it sketch the graph of y = f(cid:48)(x). Can you guess a formula for f(cid:48)(x) from its graph: find the derivative of the function using the de nition of derivative. State the domain of the function and the domain of its derivative. (a) f (x) = mx + b, where m and b are constants (b) f (x) = 1 3x: di erentiate the following functions (now you don"t have to use the de nition). (b) f (x) = (1 + x4)2/3 (c) h(t) = (t7 + 6)5(t4 + 3)2 + 1 (a) y = x + cos(x) 1 x2 x (3 + x)1/3: find the rst, second, third, and fourth derivatives of the function f (x) = xe x.
