(1) lim sin(/n®) 1/n (2) lim (n +5)7 n +00

Q: lim (In(x))½ ?

A:

Q: Q3 :(A): By using " L' Hopital rules "; Find the limits of: (1) limx-ol-cos x 2 sin²x (2) limx-0 x-³…

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Q: 2. Find if possible: sin(nx) a) lim x-4 x2-16 b) lim x (sinx+(cosx)³) (x2+1)(x-3) c) lim,--o (cosx)

A: a) Given that limx→-4sin(πx)x2-16we have to find the limit of…

Q: 5 tan(4x) x→0 3 sin(2x) Evaluate lim using L’Hôpital's rule.

A: The  L'Hopital's rule is: Suppose, f(x) and g(x) are two functions and their limit is given as:…

Q: ) lim- 1 5 arctan -4arctan |=? Use L'Hospital's Rule 4 X-0 xVx

A: L'Hospital's Rule tells us that for calculating limit of a function if we have an indeterminate form…

Q: 2 tan(x)–2x Use L'Hopital's rule to find f (x) = lim 5x3 Note: Retain any fractions in your answer.

A: f(x) = lim(x->0) (2tanx - 2x)/ 5x3 If any limit takes the indeterminate form 0/0, we can use L'…

Q: lim cos x+4e* is 5er

A:

Q: 3n Find lim„→∞ (1+)" . Hint: Apply L'Hopital's rule.

A: Please refer the attached image for complete solution.

Q: 1 2. lim cOs X -

A: The given function rewrite as

Q: 7 arctan(x) Calculate lim 0 x3 + 6x

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Q: 2) Show that sinax _a lim x-0 tanbx b %3D

A: Show that  limx→0sinaxtanbx

Q: 3) Use L'Hopital's Rule to evaluate and check your answers numerically: sin x (a) lim

A: Note: As per our company guidelines we are supposed to answer the first question only. Kindly ask…

Q: 1- cos(x/6) lim II

A: Solve the limit

Q: 3) Use L'Hopital's Rule to evaluate and check your answers numerically: 1 (b) lim x →0 sin² x 12/200…

A:

Q: 2. Find limits numerically. Use at least 3 relevant x-values for each. sin(4x) sin(4x) (a) lim x→0-…

A: Explained below

Q: 4. f(x) = cos 2 5. Find the limits, if they exist. Clearly explain how you arrived at your solution.…

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Q: F ind @ Dlim Ix16/ lim 1-cos 3x 9. 4-X lim (1-secx) lim CosO 9= (9 -) 2.

A: Note :- there is an error in part (a) in this part value of limit is wrong. So i am solving…

Q: 44. lim sin² x x→n/4

A:

Q: 9. Build a table to estimate lim sin - (Hint: Use multiples of T) (x³ - 3x2 + 6– 2x) 10. Use a table…

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Q: For question 17 –18, find the limit. sin 4x lim x>0 x 17. sec x-1 lim 18.

A: Solve for the limit

Q: 2 lim (cosx)x² =?

A: We have to find the limit

Q: Fin d the limit. lim 5x° メーッ0 Sin 3x tanx

A:

Q: Please solve asap my deadline is very close

A: We need to find limx→+∞sinx-4cosx+33x2+cos2x Consider:…

Q: Find lim 1+1? 1-e24 -2t -1 tant, 2 2 1-1

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Q: bounded on (0, 1), then lim f

A: In this question, concept of Continuity is applied. Continuity For a graph y = f(x), continuity can…

Q: 3) Use L'Hopital's Rule to evaluate and check your answers numerically: sin x (a) lim X x→0+

A: Solution: a) limx→0+sin xx1x2

Q: 1-cos (x-m) lim

A:

Q: (3) Evaluate lim -(1+sin(4))t dt

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Q: 3. Find lim x sin II

A: Given limx→∞xsin(πx)

Q: 2 lim(cosx)x² =? x→0

A: Given: limx→0cosx2x2=limx→0cos2x2x

Q: 15x 5. Find lim using special limits. X→0 sin 3x

A:

Q: Find the limit. 2+5x+ sin x lim 3 cos X 2+ 5x + sin x lim | (Type an integer or a simplified…

A: To findlimx→ 02+5x+sinx3cosx

Q: 5. Evaluate: lim, 0 2x- x2 sin a 1 Does not exist 2.

A: lim (2x-x2)/sinxx→0

Q: 3) Use L'Hopital's Rule to evaluate and check your answers numerically: (a) lim x→0+ (sina) 1 (b)…

A: Given: (a) limx→0+sin xx1x2            (b) limx→01sin2 x-1x2 To find: Evaluate using L'Hospital…

Q: 1. lim x²-1 al 2. Tく-X b) lim X-Sin 2x +3 c) lim Vey?-x

A: Given- limx→1x2-1x10-1

Q: cos x-2sinx 1. limx-n 3cosx -2 limx-3 X-3 3x6-x*+2x-3 limy--o 4x5+2x3-5 iv. lim,→-1(x³ limy--1(x³ –…

A: [i]

Q: . What is lim tan(x)? Why? 2 AY 10 8 6 4 2 -1A -0.5 0.5T, 1.57 27 2.57, 37 -4 -6

A: 1) limx→π2+tan(x)=? 2) limx→0+f(x) =? and limx→0-f(x) =?

Q: 2017 3 Example 9 Prove that lim vx +x² sin = 0.

A: Solution: The objective is to prove the given limit value is 0

Q: Find lim (e-2x cos x) (Hint: Squeeze Theor

A:

Q: Question 3 arctan(3x) lim ( Select) X--0 ex -1 1/x lim x--0+ In x ( Select)

A: to find:- limit.

Q: 2. (a) lim T-cos e (b) lim. -70 In R tim (0) メーール

A:

Q: lim cos n = 0; n-00 lim (Vn +1 – Vn) = 0. n-00

A:

Q: nx + 1 If lim エ→+0 = 9, find n. 1 %3D nx -

A:

Q: Q3 :(A): By using " L' Hopital rules "; Find the limits of: 1 2 (1) limx-o[: 1-cos x sin²x (2)…

A:

Q: 3) Use L'Hopital's Rule to evaluate and check your answers numerically: sin x (a) lim x x→0+

A: We have to determine limit by useing l hospital rule

Q: 1 x |=? Use L'Hospital's Rule 4 lim- 5 arctan -4 arctan 5 xVx

A:

Q: Evaluate

A: Our Aim is to evaluate the limit given below:-limx→0tan (2x)x-(i)