Exercise 13. Assume that f,g: [a, b] → R are differentiable on [a, b], pe (a, b). Assume that lim f(x) = lim g(x) = 0, f'(x) and = L. x-p x-p lim x→p g'(x) Prove that f(x) lim x→p g(x) = L.

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A: it is true

Q: If h(x) →5 as x→ 1 and k(x) → 0+ as h(x) k(x) X→ 1 ? x → 1, then what is lim L

A: solution:-Givenh(x)→5  as x→1k(x)→0+   as x→1

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A: Given :                     lim(x,y)→(0,0) xy4x2+y8 We know that if the limit exists, all paths…

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Q: tan(1 – x) limx→1 2 2x +x – 3,

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A: Solving by definition of 6.1.1 we have

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Q: 5) a) If a > 0, compute lim a¯*. b) Which approaches its limit faster as x→», y=2* or y=x²?

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Q: a) f(x) = 2x + 1, c = 1 [b) f(x)=3√√x+1, c = 3 4 (c) f(x) = [d) f(x) = x+1 X 1- x , C = 2 c = -3…

A: As per the guidelines I am supposed to solve only three subparts of the given problems.

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A: Given function .

Q: Lnx 8) lim 3 X X→∞

A: We will find the limit as following.