If g«EOf«) and f(x) =A. What is the value of A ? lim x+ g(x) A 0 B does not exist Infinity Finite not equal to 0

Q: Consider the piece -wise function h): = (x)4 x²-2x +3 for x 2 Find lim hx) Find is h«) Contiouous?…

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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

Q: Prove that lim, = 1, (x > 0).

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Q: Example 2. Prove that lim f(r) =1 by use of Definition 3, where f is given by - 21 +2 if a 2 f(x) =…

A: Given the proof of limx→2fx=1, where fx=x2-2x+22if x≠22if x=2 Here equation (c) is, fx-1≤32x-2 Also,…

Q: Find lim f(x) if, for all x > 1, бех 19 < f(x) < - 2ex VX - 1

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Q: Prove that if lim, „a g(x) = 0 and lim, „«f(x) exists and is not 0, then %3D f(x) lim does not exist…

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Q: lim 21/* is no limit 1

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Q: lim x-0+ \x 1 = lim x2, 1 lim x0+ x2 1 = +0 - (+0) = 0 - - - -- %3D x-0+ x

A: It is infinity minus infinity type of indeterminate form.    To solve it first convert it into 0/0…

Q: 5. If lim f(x) = 8 but lim f(x) does not exist, what can you X+2+ X+2 say about lim f(x)? X2-

A: We know that, limx→afx=l, if: limx→a+fx=limx→a-fx=l

Q: True or False: If limit as xà0 of f(x) equals zero then f(0)=0. If false provide an illustrative…

A: We will check whether the given statement is true or false.

Q: Given the function f(x) = Which f the following is/are true? (x- 1)(x + 1) 1. lim f(x) = +00 2-1+ 2.…

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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: 1. lim x²-1 al 2. Tく-X b) lim X-Sin 2x +3 c) lim Vey?-x

A: Given- limx→1x2-1x10-1

Q: 2. Consider f(x)=x² – 4x + 2 a) lim f(x) x-2 b) lim f(x) x-4 c) lim f(x) We X-1

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Q: I +b if x > 2 2) Suppose f(x) ={a if x = 2 if r < 2. (a) Find the value of b if lim f(x) exists. (b)…

A: Solution

Q: Select which of the four statements is/are TRUE? One or more options can be correct. fla + h)-f(a) A…

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Q: 1-√3-x 4. lim. x→2 4-x²

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Q: lim x3 -1 is x-1- x -1 А. — 3 B. no limit C. 3 D. undefined Е. О

A: topic - limits

Q: Use l’Hospital's Rule to show that lim 1+ X. = e. コ

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Q: if f(x) True = False 1 {} if x # 0 if x = 0 2 then_lim ƒ(x) = 0 x 0

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Q: (-x X- if x < 0 15) lim X-0 X if x 20

A: Given: limx→0-x     if x&lt;0x        if x⩾0 To Find: The value of the given limit

Q: If lim f(x) = L, then f(a) = L. X+ a A) True B) False

A: We have to check

Limits

When it comes to calculus, limits are considered to be a very important topic of discussion. The main importance of limit lies in expressing the value of a function as it gets closer to a certain value. Also, limits can help you to understand other topics, such as continuity and differentiability better. In a broader sense, every calculus notion is a limit. Other branches of calculus have also been derived from limits.