Evaluate each of the following limits. Тапx-x 1) lim x-0 x-Sinx 2) lim lnx – x² + x x-1 (x-1)2 3) lim" Tan x→0 x 2

Q: lim2

A: Explained below

Q: CONSIDER THE FOLLOWING FUNCTIONS. f22x+1 AiD gca)= xー1 a) DE TERMINE jG&) =f(x)• g(x) Lim…

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Q: b. Find lim (xv (xVx²+1-x²)

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Q: IF FLX)= and Lim F(X)6 F(-)=2 b X<l Find a,b when X#0

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Q: If 2x – 1 < (x) <x² for 0 < x < 3, find lim f(x)

A: The solution of above question is written below.

Q: Suppose lim f(x) = = x→2 1/2 4 -5, find lim x→2 x²| ƒ(x) + 6 x - 1

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Q: V6 - 5x , x > -1 Determine lim x-2 wheref ( x %3D 2x2 - 5x , x < -1

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Q: x²+x-2 1. lim X-o 4x-1

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Q: Find 2-Vx2-5 lim X-1 x+3

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Q: Guess the value of lim x 0 (tanx-x)/x3

A: Given :          limx→0tanx-xx3

Q: V5x+4-3 3) lim X-1 x-1

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Q: 4. Find: b) lime X0 x sinx

A: Find the limit by using L'  Hospital rule

Q: If lim x-4 x-2 f(x)-5 - =1, find lim f(x) X-4

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Q: Evaluate lim h→0 1 2 5 (x+h) ² 2h 1 5x²

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Q: Calculate lim X→-2 x³ + 2x² - 1 5 - 3x

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Q: Find lim x+x:

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Q: Find the limits lim x→1- sin-1x

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Q: If 2x - 2s f(x) S x² - 2x + 2 for x 2 0, find lim f(x) x-2

A: see below the answer

Q: 2x a. lim x-+3" X - 3

A: limit

Q: x* + x² - 1 Find lim XC

A: Please see the explanation below

Q: x - 5 lim x→5 x² – 25

A: Explanation of the solution is given below...

Q: 3x 2х 2) Lim х-1 х+1° X → 00

A: Given,   limx→∞(3xx-1-2xx+1)

Q: 3x(x - : lim Tx - 1| X1+

A: Replace the value of the limit and x.