Suppose that lim f(x) = 0, lim g(x) = 0, lim h(x) = 1, lim p(x) = ∞, and x→a x→a x→a x→a lim q(x) = ∞. x→a Evaluate each of the following limits. (a) lim [f(x)]⁹(*) x→a = (b) lim [f(x)]P(x) = x→a (c) lim [h(x)]P(x) x→a =

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A: A function f(x) is differentiable at x=a, if limit exist at x=a and is equal to f(a)

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Q: If lim f(x) = 2, and lim g(x) = 7 find: C→C I-C a) lim 4f(z) A C b) lim ln(g(x))

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A:

Q: 3) If the lim f(x) = 2 and lim f(x) = -1 %3D x-3- x-3+ Then what is the lim f (x) = x→3 %3D a) Why?

A: To find the limit of the f(x) at x=3

Q: . Let (x2 + 1 f(x) = 1( - 2)² if x> 1 if x<1 (a) Find lim,-I- f(x) and lim,→* f(x). (b) Does lim ,1…

A: Given: For (a),     limx→1- f(x)=limx→1 x2+1=12+1=2 and     limx→1+ f(x)=limx→1 x-22=(-1)2 =1

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Q: If lim f(x)=-2 and lim g(x) = 2, what is the value of lim [f (x)+2g(x)]?

A: Given, limx→afx=-2  and  limx→agx=2

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A: Here we use sandwich theorem Also known as squeeze theoremThis theorem states that , if gx≤fx≤hx in…

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Q: Suppose ƒ: (0, ∞) → (0, ∞) is a function such that lim f(x) exists 2+0 and equals 4. True or false:…

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