Sfsin(r – y kýyd . B. (i) Evaluate 00 sVx+1 lim (ii) Evaluate * 4Vx +3

Q: 2) Show that the_lim. 1) xy2 lim (x,y)→(0,0) x² +y²

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Q: Evaluate the limit. x² +3x - 10 lim-5 2x + 10

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Q: 3. Find lim (x² + 3x – 18)/(x – 3)-

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Q: Evaluate the limit: 4x + 4 lim x -1 x2 -2x-3 %3D

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Q: 4-x lim,.

A: The given limit is limx→∞4-xx

Q: 1. Use the definition to show that x² - y² lim (x,y)→(0,0) x² - y² = 0.

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Q: Evaluate the lim x + 3 2r2 – 3x + 1 5x +4

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Q: If 3x - 4 s f(x) sx2 - 3x + 5 for x 2 0, find lim f(x). x-3

A: Given, 3x-4 ≤ fx ≤ x2-3x+5              for  x ≥ 0 We have to find limx→3fx

Q: Show that lim Z-2 (2-2)4 || ∞

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Q: evaluate the Ilimits 3. X+2x 2. lim メー→○ X42x

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Q: b. Find lim (xv (xVx²+1-x²)

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Q: Evaluate the limit. +4-2 limx→0

A: First rationalize the numerator.

Q: Evaluate the limit: 1 2 (2+y) 1 4 lim

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Q: Find the limit. 3) lim Vx2 + 5x - Vx2 - 3x X00

A: To find the given limit.limx→∞x2+5x-x2-3x

Q: Evaluate the limit. Vx2 lim x² + 3 3x2 + 1 x- 00

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Q: Use continuity to evaluate the limit. 32 + Vx lim x→4 32 + X

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Q: evaluate the limit lim (x + 1)(3x^2 − 9) x→2

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Q: Evaluate the limit: lim 8y2 - 5y: y 2 %3D

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Q: If 7-6x2 sf(x)s 7-x² for -1sxs 1, find lim f(x). X→0 lim f(x) =

A: If 7-6x2≤f(x)≤7-x2 for -1≤x≤1, we have to find limx→0f(x)

Q: Evaluate the limit. 3x3 – 5x² + 1 lim 00-X V2x6 – 4x + 3

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Q: Evaluate the limit. 2x5–16x² lim→2 2.2+ a³

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Q: Evaluate the limit lim (16y + 1)(2y1/2 + 1) y→1/4

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Q: If y = vb2 + x2 and y + Ay = Vb² + (x + Ax)² , what is the lim Y ? Ax0 Ax Select the correct…

A: Given, y=√(b2+x2) Δy=√[b2+(x+Δx)2]

Q: Find the limit. lim              x2+5/5x3-2 x→+∞

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Q: O Find 2- X Lim X→2 2- 2X X #2 xY _ 2x² – 8 x² - 4 2 Find Lim x²- 2x²- 8 X->2 Lim 3X X→3 X- 3 -3 X…

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

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Q: メ-D4 xー12 In do torminate Form Lim | १ - 3

A: Given:   Limit equation is given

Q: Use a u substitution to find Vx – 7 – 2 lim | x-15 x – 15

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Q: Find the exists. 5 x а. lim 3 5x'+1 b. lim 10х-3x +7

A: Given that: a. limx→-∞5x-x3b. limx→∞5x3+110x3-3x2+7c. limx→∞5x2+2x2+3

Q: Evaluate using substitution.

A: To find limx→2x3+4x Substitute x = 2 in x3+4x                    limx→2x3+4x=23+4(2)…

Q: Evaluate the limit. Vx2 + 3 lim 3x2 + 1

A: Given that a limit problem and we solve this problem by using general property of limit.     Here i…

Q: Evaluate the limit 7x3 – 2x2 – 2x lim 2 — 4х — За3 x → 00

A: limx→∞7x3-2x2-2x2-4x-3x3 ⇒ limx→∞7-21x-21x221x3-41x2-3 (divide numerator and denominator by x3)

Q: f-x² + 10x - 25 < g(x) < a² - < 10x + 25 for 4 <x 6, evaluate lim, →5 9(x).

A:

Q: Evaluate the indicated limits 3z – 5z² + 7 (i) lim 1-400 8+ 2x – 5x4 lim

A: To find: limit of the given function

Q: Find the limit. 4 lim x→-2+ x + 2

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Q: Evaluate the limit 7x2 2.0 2x +3 lim 3x +4

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Q: Evaluate the limit. 4x2-9 lim x→3/2 15-10x а. b. lim(x – 2) sec(n/x) | x-2

A: See the details solution in below

Q: 4x2-x- V9x2 –x lim

A: Given: limx→∞4x2-x-9x2-xx

Q: Evaluate the limit 4)². 2 + 4 16 lim

A: we have to find out the limit of given question

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

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

Q: If /10 - 7x sf(x)s/10 -x for -15xs1, find lim f(x). x-0

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Q: (3+x)² – 9 - Compute lim

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Q: Determine limx→−2 6/x-2, if it exists

A: limx→−2 6/x-2 yes limit exist and we can direct apply the limit so put -2 in given function…

Q: 6. Find lim Vx -4 Vx - x>16 x– 16

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Q: Find the limit or show that it does not exist. lim √25t² + 2 − 5t t-x

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Q: Find Vx2 +8-3 lim x--1 x +1

A: we have to solve the given limit . so , we rationalise the numerator .

Q: Find the limit:    limx 2(4x2 + 3).

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Q: 7. Evaluate the limit: 9x2 -2 lim 2 3x 2 x-3

A: To evaluate the limit:limx→239x2-22-3x Solution: It is 00 form. We will use L-hospital rule. In…

Q: Use the definition to show that x² - y² lim (x,y) →(0,0) x² - y² 0.

A: