| kx – 3, r<–1 r² + k, r > -1' Given f(x) = find the value of k such that lim f(x) exists.

Q: Consider the function f(x)=(x4 -2x3)/(x-2). Verify that Lim (x->2) f(x)=8. In order to guarantee…

A: Consider the function f(x)=(x4 -2x3)/(x-2). To Verify that limx→2f(x) = 8

Q: (a) lim [f(x) + 3g(x)]

A: Given:  limx→2  fx=1,  limx→2  gx=-2,  limx→2  hx=0 To Find:  limx→2  fx+3gx=?

Q: If V 16x <f(x)sx+4 for all positive x-values, then what is lim f(x)?

A:

Q: Given that f(x) = 2x² +1, find:“ f(x+h)- f(x) f(x+h)– f(x). lim h→0 h h

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Q: g(x)= 7 lim x→7 √g(x)

A:

Q: 3x3 - 4x lim 5x³ – 2 ,3 X→-0

A: Given limit is as below:

Q: If f and g are continuous functions with f(3) = 5 and lim,- [2f(x) – g(x)] = 4, find g(3).

A: Use the fact that limx→cfx+gx=limx→cfx+limx→cgx. Also, limx→ccfx=climx→cfx Now,…

Q: Evaluate: * х — 5 lim х-5 Vx+4 – 3

A:

Q: If 3x – 1 0, find lim f(x). X→3

A: Given query is to find the indicated limit.

Q: Find Lim-0.0 (r² + y²) In(x² +y²) '(xy)(0,0)

A:

Q: 7x f h(x) = (1 + 4) ¹*, find lim h(x). X→∞

A: Please see the below picture for detailed solution.

Q: 16-x2| (a) lim (2 + x) 16-x²| ズ→4+ 4-x

A: Given query is to find the limit of the expression.

Q: For the function f(x) = 2/x, calculate lim h->0 (f(1+h) - f(1)) / h

A: Given function:- fx=2x

Q: Given f(x) = 7x - 6; x < 6 x ≥ 6, 4x + 3 ; Find: lim x →6 f(x)

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Q: find the limit

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Q: If f(x) = Vx² + x – x, find lim f (x), where f(x) is defined at X → 0.

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Q: limits

A: L'Hospital's rule apply only when there is 0/0 for ∞/∞ form.

Q: If 3x − 1 ≤ f(x) ≤ x2 − 3x + 8 for x ≥ 0, find lim x→3 f(x).

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

Q: If 2x – 2 0, find limf (x). x→1

A: We can use the sandwich theorem to solve this question.

Q: Find lim x+x:

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Q: The expression limħ→0 f(a+h)-f(x) gives the slope of the line tangent to a function at the point h…

A: