Q10 Consider the piecewise function below. x ≤ 0 f(x) = x² 3, - 19 - X X " Definition: lim f(x) exists if all the followings hold: x-a (a) lim f(x) exists. x-α- 0 < x < 4. x > 4 (b) lim f(x) exists. x→a+ (c) lim f(x) = lim f(x) x-a x→a+ Use the above definition to answer the following questions. a) Determine whether lim f(x) exists. x-0 b) Determine whether the limit of f exists when a approaches 4.

Q: * +3 ,x1 „x>1 g(x) exists? Justify. 1+1 f(x) a) Does lim f(x) + g(x) exists? Justify. b) Does lim

A: Solve the given function

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Q: x+x? ii] lim 3-x

A: we have to find the limits algebraically

Q: 2)

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A: Given, limh→ 0h+13-1h+1-1

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A: Consider a function fx. The lim f(x) as x approaches to c is said to exist when the right hand limit…

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Q: Let f(x) be the following piece wise function f(x) = ( x ² + => if 0 1 Show lim f(x) does not exist…

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Q: 11. Consider the function f(x) = x³-ax²-x+b X+1 lim f(x) exists, determine all value(s) of lim f(x).…

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Q: f(x) . If lim x→0 x? 1, find a. lim f(x) x→0 f(x) b. lim x→0

A: To find the value of the given limits .

Q: Find the area of the region bounded by the graphs of the functions y=9-x² and y=x+3.

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Q: S 1.4x + 0.8, x -2 f(-2) = lim f(x) = x--2- lim f(x) = x--2+ lim f(x) = || x--2

A: E

Q: ズー1 2. lim X-3 エ+1

A: Consider the provided expression, limx→3x-1x+1 Evaluate the above limit.

Q: x+2 = +2| Does lim f(x) exist? Give reasons for your conclusion. Consider the function f (x) 2. x-2

A: We will calculate the limit

Q: Evaluate Lim マ-1 X-1 区 -1

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Q: .Using &-8 definition show that x3 – 4 lim x→2 x2 + 1 - 4 4 - + in

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Q: If lim x→0 a) f(x) x = 1 and lim x-0 lim g(x) x→0 g(x) – 2, evaluate: X b) lim x-0 g(x) f(x)

A: NOTE: Refresh your page if you can't see any equations. . here we have

Q: If f(x) = x² then lim f(x) – f(2) = 0 . x – 2

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Q: Find lim,-2 f(x) 2 -3 -2 -1 2 3 lim→-2 f(x) = 0 %3D lim, -2 f(x) = 2 lim,-2 f(x) = 1 Does Not exist

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Q: x° - 27 (b) lim x² -9 x→3

A: Given, limx→3x3-27x2-9

Q: Find all values of a and b that make -a - x, x< -2 /(x) = { Vx + b, bx² + 1, -2 Sx<1 x21 continuous…

A: Given:             fx=-a-x,            x&lt;-2bx2+1,    -2≤x&lt;1x+b,        x≥1

Q: Vx+5-3 (a) Find lim,4 analytically. X-4 Vx+5-3 -, x * 4 (b) Let f(x) = x-4 13, x = 4 Use the three…

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