Let f(x)= {x2+4sec(pix) if 5/3 ≤ x < 3 , -2x+7 if x>3 a. Find lim f(x) and lim f(x) x→3+ x→3− b. Find lim f(x) or explain why it does not exist.

Q: Find the limit for when x -> 4 lim F(x), for f(x)= x2+2 ; x≠4 ; 27; x=4

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Q: Suppose that lim 4f(x)+ 2x – 14 5. Find lim f(x). z→1 %3D z→1 x – 1

A: Given

Q: Estimate the limit numerically if it exists. (If an answer does not exist, enter DNE.) lim x→+∞  7x2…

A: The given expression of the limit is: limx→+∞7x2+10x-12x2-2x

Q: Consider f(x)=x−9/x+4 a) As x→∞, f(x)→ b) As x→−∞, f(x)→ f(x)=10x+7/x−6 c)limx→∞f(x)=

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Q: If / 10 - 7x2 sf(x)s/10 – x² for - 1<x<1, find lim f(x). lim f(x) = x→0

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Q: lim x² ln x x-0*

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Q: Estimate the limit numerically. x² lim +14x+49 -7 x+7 O-7 Oto∞ O-1 00

A: Given limit is We will use the factorization method to evaluate the limit By using the result that…

Q: Suppose that limx→0f(x)=π. Select the best answer below.  3.14<f(x)<π  on some interval  (−δ,δ)…

A: Suppose that limx→0f(x)=π. Then 3.14&lt;f(x)&lt;3.15 on the  interval  (−10−15,10−15)…

Q: Evaluate lim f(x), where f(x) = e value of "p" assuming that lim f(x) exists. Nx + (M + 77) if x<5…

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Q: Find lim f(x) for the given piecewise function. x-4 2x +2 if x 4 If the limit does not exist, enter…

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Q: Find Limit Using Squeeze Theorem: 2. If 2x – 2s f(x)<x² – 4x + 3 for x 2 0, find lim f(x).

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Q: If ƒ(1) = 5, must limxS1 ƒ(x) exist? If it does, then must limxS1 ƒ(x) = 5? Can we conclude anything…

A: A function f(x) is said to be continuous at a point x = a, in its domain if the following three…

Q: Suppose a is a constant and if x> 3 f(x) = {x? if 2 <x< 3 x+a ifx< 2. (i) Find lim f(x). X+2+ (ii)…

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Q: Let F(x) = (x2 + 3x + 2)/(2 - | x | ). Make tables of values of F at values of x that approach c =…

A: Given: Fx=x2+3x+22-x To determine: We have to estimate limx→-2Fx by making a table of values of F at…

Q: Estimate the limit numerically if it exists. (If an answer does not exist, enter DNE.) lim x→+∞  5x2…

A: Consider the given function:

Q: a. Evaluate limx→5 f(x), where f(x) = { 11x+ (2 +77) Ef x5 f(x) exists.

A: solution is given below..

Q: Evaluate the limit numerically: lim x → 3 f ( x ), where f ( x ) = { x 2 − 4 x + 2 x < 3 − x 2 + 8 x…

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Q: If f (x) = −x + 8 for x ≤0 and f (x) = 4x + 7 for x > 0, find (a) limx→0+ f (x) (b) limx→0− f (x)

A: We can find the limit as below.

Q: Find the limit. lim x2/(1-x) X→1 *

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Q: Find the limit of the function lim x² 3x +2 X-1 X-A

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Q: Evaluate the limit. limx→2 e^x^2−e^4/ x^2 −2x

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Q: If 3x s f(x) sx +2 for 0sxs 2, evaluate lim f(x).

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Q: If 2x+2 ≤ f(x) ≤ x2 +2x+2, for all x, then find lim f(x) x-> 0

A: Given

Q: what is the lim x->0  f(x)-f(0)/x^2 if f(x)=2x^2+1?

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Q: If Lim [x3 – g(x)] = 12 as x tends to 3, use the Rules of Limits to find Lim g(x) as x tends to 3.…

A: Given: limx→3x3-gx=12

Q: Find the limit of lim((9+3x)1/2-3)/x as x approaches 0

A: To determine the value of the limit.

Q: Suppose a is a constant and if x>3 f(x) = { if 2 <x<3 %3D x+a if x < 2. () Find lim f(x). X2+ (ii)…

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Q: If 1/(x^2 + 1) ≤ f(x) ≤ 1 + x^2 for all x in the interval (−1, 1), what is lim x→0 f(x)?

A: Please refer the attached image for complete solution.

Q: Given f(x) = 3/(4-x)3 , evaluate limx=4+ f(x)

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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: For f(x) = (-x^3+1) / (2x+8), evaluate limx→∞ f(x) and limx→−∞ f(x). Then give the horizontal…

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Q: Use lim f(x) = -2 and lim g(x) = 5 to find the limit. %3D lim [3f(x) – 4g(x)]

A: The given limits are limx→cf(x)=-2 and limx→cg(x)=5

Q: For f(x) = −x^3 + 1/2x + 8 evaluate limx→∞ f(x) and limx→−∞ f(x). Then give the horizontal asymptote…

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Q: Consider a function x-1 if x 1 (a) Find lim f (x) if it exists. If it doesn't exist, explain why.…

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Q: . Is it possible that f(2) = 5 but limx→2 f(x) = 7? If so, what kind of function can satisfy this?

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Q: Find the limit: limx 1(x2 + x + 2)/( x + 1)

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Q: Suppose that limx→ -2 p(x) = 4, limx→ -2 r(x) = 0, andlimx→ -2 s(x) = -3. Find lim x→ -2 (-4p(x) +…

A: Given limx→-2p(x)=-4 , limx→-2r(x)=0 and limx→-2s(x)=-3We need to find:limx→-2-4p(x)+5r(x)s(x)

Q: Suppose that limx→ -2 p(x) = 4, limx→ -2 r(x) = 0, andlimx→ -2 s(x) = -3. Find lim x→ -2 (p(x) +…

A: Suppose that limx→ -2 p(x) = 4, limx→ -2 r(x) = 0, andlimx→ -2 s(x) = -3. Find limx→ -2(p(x) + r(x)…

Q: Find the constant c so that the limit limx->3 (x2+x+c)/(x2-5x+6) exists.

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Q: Find the limit. (a) lim x→3 Vx +6 – x x3 – 3x2

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Q: If lim (x approaches 6) (f(x)-4)/(x-3)= 2, how do I find lim (x approaches 6) f(x)?

A: We separate the limit first.

Q: Estimate the limit numerically if it exists. (If an answer does not exist, enter DNE.) lim x→+∞  5x2…

A: The given limit of expression is lim x→∞+5x2+5x-42x2-3x Divide the expression by highest denominator…

Q: Suppose limy-e- f(x) = I and limx-e- g(x) = m. Prove that limxe-(3f (x) + 4g(x)) = 31 + 4m.

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Q: Evaluate the limit 5 + 2x lim 8 – 8x x → 0

A: We haven the function is: f(x) = (5 + 2x)/(8 - 8x)  Dividing the numerator and the denominator by x…

Q: Use the Squeeze Theorem to find limx→8f(x), given that  2−|x−8|≤f(x)≤2+|x−8|.   limx→8f(x)=

A: To use the Squeeze Theorem to find limx→8f(x), given that  2−|x−8|≤f(x)≤2+|x−8|.

Q: use f(x) to find: limx→0f(x), limx→-4f(x), limx→5+f(x), limx→-4-f(x). the discontinuity that is…

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Q: Let f(x) = x^2 − 10x. If you construct an ϵ-δ proof to show that limx→5 f(x) = −25, what is the…

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Q: Q2: Use lim x 0 and lim x 0 to show that lim x = 0.

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Q: Suppose g(x) is a function. sin(32) If lim 9(x)+ =8, then what is lim g(x) ? Your answer should be…

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