iv. lim x' -2x² X -00 v. lim 3x – Vx* – 2x +3 lim I-0 x vi.

Q: Q.3 Find the following limits: x+3 3.1 lim→-3 x2+4x+3 x² +4x+3 x+2 3.2 limx-2 Jx² +5-3 u-1 3.3 lim-1…

A: As per the company guidelines we can solve first three parts . I hope that the given solution will…

Q: Use l'Hôpital's rule to find the following limit. 3x-2x lim 3 X o 5x° +3

A: To use the L-Hospital rule to find  Lim(x tends to infinity) [3x³-2x]/[5x³+3]

Q: 4) Use L'Hosp9tal's Rule to find the limits c) lim tanx)) メ→0 d) lim (ex + メ メ→ o

A:

Q: Evaluate the following limits by applying the L'Hopital's rule only. x³ + 3x² – 54) lim x→3 3 Vx5 –…

A: F

Q: 1 Use l'Hopital's rule to evaluate lim 1+0+ \I In(1 + x),

A: Question is solved.

Q: Determine the following limits by using L'Hôpital's Rule, if exists. 1- x + ln x (a) lim 1³-3x+2 (b)…

A:

Q: B) Evaluate two of the following limits (Without using calcu 1 1) lim 1-cos2 x

A:

Q: Evaluate the limit using L’Hôpital’s Rule

A:

Q: 3x lim 20 et – 1

A:

Q: Find lim (2+x)" * using L'Hôpital's rule. 1/x

A: Given the given expression is limx→∞2+x1x.

Q: (a) Determine the following limits without using L'Hôpital's rule. V7x° +4x -x² -2 lim x'-2x-3x+1…

A:

Q: Find the limits by using L.Hopital rule : 7x 1. lim x-0 sin 2x x2-16 2. lim x4 (Vx+5)-3

A: We need to find the limits of the given expressions by using the L.Hopital rule. For (1),

Q: (c) Find the following limits WITHOUT using the L’Hopital's Rule. -5x2-8 lim x→+∞ 2x+3 (i) Зx+1-сos…

A: According to our guidelines we can answer only three subparts, or first question and rest can be…

Q: 2. Calculate the following limits. Justify your answer. L'Hopital's rule Rule ) (without using 2x +1…

A:

Q: 12, Show that the following limits do not exist. (а) lim 1 (x > 0), (b) lim (x > 0), x-0x2 x-0 Vx…

A: Given: d) limx→0sin1x2 to prove limit does not exist.

Q: Find the value of the following limits: 5y 1-limy→o tan 10y 2-limx-0 6x cot3x 7x²+8x 3-limx-0 4x²…

A:

Q: 2x + 1 (a) lim 9x2+ x

A: We have to solve the limit

Q: 8. Evaluate the limits by previous methods or by L'Hospital's Rule, if applicable: 4x3 +3x 4x b) lim…

A: We have to find limit

Q: Use l'Hôpital's Rule to evaluate the limit. 2 - 4x+2 lim 2. X>co X+5x+11

A: The limit of a function limx→Xfx=Y means that value of  function fx can be as close to Y by making…

Q: Express the limit as a definite integral. lim xk Ax [-3, 2] 4-0 k 1

A: Given

Q: b) Use L'Hopital's rule to find the limit: 1/In x (In xv lim

A:

Q: 2. Calculate the following limits. Justify your answer. (without using L'Hopital's rule Rule or…

A:

Q: 1. Use L'Hopital's Rule to calculate the following limits: (a) lim,0+ xsim. (b) lim, 1- T/2-sin-1r…

A:

Q: 5x2 + 10x + 1 20. lim x* + x² + 1

A:

Q: 5. Apply L'Hopital's rule to determine the limits of the function. y = lim e"(x – a² + 9)

A:

Q: 5. Show that x³y³ lim (x,y) →(0,0) 2x¹2 + 3y4 does not exist.

A:

Q: Зx+1-сosx lim 3 3x-5 lim x→-0 6х+8 lim 3x – Vx4 – 2x + 3

A:

Q: Find the limits. sinh 3x 1) lim arctan 2x

A: We have to find limit

Q: Q3. Compute the following limits if they exist. SEC x – 1 (а) lim x→0- sin x (b) lim x→0 x tan x 2 -…

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Q: In(1+ x?) lim x-0 x3

A:

Q: B) Find the limits by using L.Hopital rule: 7x 1. lim X0 sin 2x x2-16 2. lim X+4 (VI+5)-3

A: *to find :- limits, using L-Hopital rule.

Q: Find the limit.   Lim x→∞             (1+2x)5/2 ln x

A:

Q: Use l’Hôpital’s rule to find the limits

A:

Q: 2. Find the limit of the following function by using L’Hopital's Rule. In x lim - х>0 CSC X

A:

Q: Express the limit as a definite integral on the given interval. lim S 19(x/)³ – 8x;]Ax, [2, 5] 1

A: The definition of definite integral is, ∫abf(x) dx = limn→∞ ∑i=1n f(xi*)△x   in the interval a, b…

Q: x²-4x lim |x| (i)

A: Here we calculate the limit and here x is non positive because x tends to 0 negative.

Q: Q2: (a) By using " L' Hopital rul (1) limx¬(1/2)-(tan x)cos x

A:

Q: (b) Find the following limits WITHOUT using the L'Hopital’s Rule. x² –4x lim x→0- ]x| (i) 2tan?x lim…

A: (1). From the given problem: limx→0-x2-4xx

Q: x2 + 2x + 1 lim x--2 x2 + x +1

A: There is no need for L hospital as the limit can be evaluated directly.

Q: 2. Calculate the following limits. sin 3x a) lim х-0 2х(х-3) V4+h-2 b) lim h→0 h 5х-4 c) lim X→∞…

A:

Q: x – 4 lim 244 x2 – 3x – 4

A:

Q: Evaluate the following limits: x – 25 (i) lim x+25 Vx – 5 Vx² – 3 (iii) lim x→-o 4x +5 sin(50) х — 3…

A: Since you have posted a question with multiple sub-parts, we will solve first three sub-parts for…

Q: B) Find the limits by using L.Hopital rule : 7x 1. lim 0 sin 2 -16 2. lim 4 (V+5)-3

A: 1. Here limx→07xsin 2x is of 00 form, so by applying L. hospital rule, we get limx→07xsin 2x =…

Q: lim vii.

A: To find:-

Q: Use l’Hôpital’s rule to find the limits

A:

Q: Use l’Hôpital’s rule to find the limits

A: Let the given limit be L - L = limx→0 x2lnsecxUsing L-hospital rule, differentiating numerator and…

Q: -x e lim In(1+4e-x)

A: The answer is 1/4

Q: -5x²-8 lim x→+0 2x+3

A: To find the limit in a given problem.

Q: Express the limit as a definite integral on the given interval. lim [9(x*)³ - 2x*JAx, [2, 9]

A:

Q: 5x2 + 10х + 1 :0. lim x4 + x? + 1

A: