Use algebraic manipulations and limit laws to evaluate the following: (a) Find limx→∞ √x + 9-√√x (x+1)²(x-1)5 (b) Find limx→-3) (x-4)³(x+3)²

Q: sin 04) find limx-2n 2x-4n S0 (x²+x+1)* Q5) lim- (r²+1)100

A: In the given question we have to find the limit of the question 4 and question 5. the question 4 is…

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

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Q: 1-3x limx-0 V5x2+2 Select one: О а. 5 -3 O b. 5 C. O d. 5 O e. none

A: Divide both numerator and denominator by x and use the limit

Q: points

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Q: Q.2.(a) Evaluate: t2+t-2 lime1 t2-1

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Q: -e g). lim [In(6x² + 5) – In(3x² – 6)] h). lim ズ→の

A: g) limx→∞ln6x2+5-ln3x2-6h) limx→-∞e2x-e-2xe2x+e-2x

Q: Calculate the limit limx→0lncosx3√1+x2−1.

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Q: Evaluate using the identity a3-b3 = (a-b)(a2+ab+b2)

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Q: Find the limit

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Q: 25) Find: lim,(x²+ax - √x² + bx).

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Q: X 2 +2 x-2 3. Find lim 4. Prove that lim(2x² +1)=3

A: Dear student,                       According to our guidelines we are supposed to answer only first…

Q: 19. Evaluate lim (x³ + 2x2 – 3x – 4). x-1

A: Evaluate limx→-1(x3+2x2-3x-4)

Q: (e) lim (3x²-x¹ + 1) 818

A: Given Limit,e. limx→∞3x2 - x4 +1

Q: If limz - - 19+561 (z² + 38z) = x + iy, what is the value of x - y ?

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Q: 200 (-1) = 1, lim (x – 2) = + Use the results that = 1, lim (x – 2) = +∞ lim I+3 T-1 エ→8 エ→0 to find…

A: Given that limx→∞(x+3x-1)=1and limx→∞(x-2)=+∞Required to…

Q: Evaluate using the identity: a3 − b3 = (a − b)(a2 + ab + b2)

A: Given, limx→1x4-1x3-1. The objective is to evaluate the limit.   Apply the identity: x2-y2=x+yx-y…

Q: 6. Find the lim (x²-3)³ (x³ + 2)²x

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Q: The value of lim (x³+2x4- 7x3- 5x²+ 11x – 15) X--2 (A) - 1 B) 1 2 (D -5

A: We need to evaluate limx→-2 x5+2x4-7x3-5x2+11x-15

Q: (b) lim In(5x2 +3) – In(2r² + 1). -

A: Given :

Q: [a] find limg00 a+[b] *

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Q: Evaluate using the identity a3-b3 = (a-b)(a2+ab+b2)

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Q: Find the following: x1/3 + 9x1/5 (2х — 1)1/2 — 3 - i. Lim 6x1/2 – 4x1/4 ii. Lim x→5+ х — 5

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Q: Find the lim (√9x² + x - 3x)

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Q: Find the following: x1/3 + 9x1/5 i. Lim х-0 6х1/2 — 4х1/4 ii. Lim х+5+ (2х — 1)1/2 — 3 х — 5

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Q: 4/2+81x 3 X→∞0 X +7 Find lim lim X→∞0 2+81x 3 X +7 = (Simplify your answer.)

A: Given query is to find indicated limit.