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Finding Functions Find functions f and g such that
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- (a) Suppose you have two functions f(x) and g(x), with f(x) # g(x) and you know for f(x), ? Explain with examples. x-0o g(x) certain that lim f(x) =∞ and lim g(x) : =o. What is lim x-00 (b) The two functions f(x) and g(x) shown in the picture are linear. (And they are not the same functions as the ones in part (a) above.) gex) With the information as labeled in the figure and the facts lim f(x) = 0 and lim g(x) = 0, evaluate x-a f(x) lim x-a g(x) or explain why you don't have enough information. Clearly state all your reasoning.arrow_forwardB The graph of a function f with f (b) > f (a) is shown above for a ≤ x ≤ b. The derivative of f exists for all x in the interval a < x < b except x = 0. For how many values of c, for a < c < b, does lim f(x)-f(c) f(b)-f(a) x-c b-a X-C Zero Two Three (a, f(a)) Four = (b, f(b)) ? Varrow_forwardƒ(x) − ƒ(−1) x+1 7. If f(x) = (x²+1) what is lim x-1 (A) -24 (B) -8 (C) 0 ? (D) 12arrow_forward
- If lim f(x) = 14 and lim g(x) = 22 then x→7 x→7 lim[4f(x)g(x) – 7] = %3D - x→7 1225 210 1239 28 1232arrow_forward747 Use the graph of y = f (x) to find the best possible answer for each of the following. Use o, -00, or DNE (“Does Not Exist") where appropriate. You de - %3D --- - fa -thicuecticarrow_forwardLet f, g and h be functions defined on R \ {0} such that both f and h are even functions, g is an odd function, h(x)+ 2 = 3. lim f(x) = a, lim g(x) = b, and lim Find lim [g(x)(f(x) – h(x))]. x -00arrow_forward
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