1 (*+ stn) (x + sin- lim x→+∞ X.

Q: Evaluate the limit: sin(2x) cos(5x) lim

A: Given,           limx→0sin2xcos5xx

Q: 4) Find the value of a for which the limit lim x→0 evaluate the limit. sin(ax)-sinx-x x3 is finite…

A: To Find: The value of a for which the limit limx→0sin(ax)-sin(x)-xx3 is finite and then evaluate the…

Q: Evaluate the limit: sin 7z sin 4x lim sin 4z sin 2r

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Q: Find the limit. 15) lim V3 + cos2 x A) 2 16) lim (3 sin x - 1)

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Q: 9. Evaluate the limit. lim (1+ sin 3x)1/x x→0+

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Q: lim sin (-2 T x) = x → -3

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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: Compute, from first principles, without using L'Hopital's rule eh – 1 lim = 1 h-0 h

A: (18) We have to evaluate the limh→0eh−1h. We know that the expansion of eh, which is given by…

Q: lim X(In x)2 requires repeated application of L'Hopital's rule. Show all the steps.

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: ,3x lim x→0 CO cosh(Зa)

A: By substituting cosh(3x) in givenimit we can get the required value of Function.

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

A:

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

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Q: 4. Use L'Hopital's rule to evaluate sinh(2) lim x+0 sec(x) - 1

A: we have to evaluate  limx→0sinh2xsecx-1=00 It is known that ddxsecx=secx tanxddxsinhx=coshxddxtan…

Q: Compute the limit as x goes to 0 of [tan(x) - sin(3x)] / (x^2)

A: limx→0[tan(x)-sin(3x)]x2=[tan(0)-sin(3(0))]02=00

Q: Use L'Hopital's rule to evaluate lim(1 – 2 sinh(x)) sch(a).

A:

Q: tan(1 – x) 2 limx→1 2x +x – 3

A:

Q: 1. To take the derivative of the following function. х т (1) y = m (2) y = x' log 2. To find out the…

A:

Q: Find the following limit: x3 – 7x + 6 1) lim x-1 x2 - 3x + 2 sinx 2) lim x0 tan4x V2 - x - x 3) lim…

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Q: Evaluate the limit (1 – cos x)² sin² . lim x2(1 – e)4 COS X - -

A: Given limit is : limx→01-cosx2sin2xx21-ex4  To find the value of the limit.

Q: B) Find the limits by using L.Hopital rule: 7x 1. lim x-0 sin 2x x2-16 2. lim x-4 (Vx+5)-3

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Q: Compute lim 2>0 sin x O 2 O-1 1 undefined

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Q: Determine the following limits analytically.

A: Given: The limit expression limx→π21-sin3xcos2x, To find: The value of given expression.

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

A:

Q: 3. Find the limit. tan(5x) 0 sin(3x) sin(6x) (2) lim x04x-5x (1) lim

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Q: 12. Evaluate the limit n Σ lim -> sin(- n→∞ N k=1 by expressing it as an integral.

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Q: compute limit as x goes to 0 of (sin(x)-x)/(x^3)

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Q: Find the limit. sinx cos 4x lim x-0 x + x cos 5x A) 3 B) 0 C) D) Does not exist 4/5 -/2

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Q: cosx * sin? (3x) 2 2. lim x→0 x2

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Q: Express the limit as a definite integral on the given interval. lim 21 (x)2 + 7 Ax, [1, 8] dx

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Q: (sin 2x)* - 4x →0+ x -

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

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

A: We have to find the limit using L Hospital rule.

Q: find the limit as x approaches 0. 12sin(3x)/1-cos(3x) = as x approaches 0

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Q: Prove rigorously that lim sin 1/x does not exist.                                    x → 0

A: Let the given limit be y - y = limx→0 sin1xy = limx→0 sin1x1x×1xy = limx→0 sin1x1x×limx→0 1xy =…

Q: lim(cos' x+sin 5x) tan 3x x→0

A: Given- limx→0cos3x+sin5x2tan3x To Find- The value of the above limit.

Q: Q1- Evaluate the limit :- 1- lim - ( - cos) (1+ sin ) ) (1 + sin±)

A: “Since you have asked multiple question, we will solve the first question for you. If you want any…

Q: f (x) = 4 sin(3x + 7) is continuous at every point x = x0; that is, lim 4 sin(3x + 1) = 4 sin(3xo +…

A:

Q: Find the limit. lim x→4  sin(x − 4) x2 + 5x − 36

A: To Determine: find the limit of  limx→4sin(x-4)x2+5x-36 Given: welimx→4sin(x-4)x2+5x-36 Explanation:…

Q: Find the tangent equation for the function: f(x) = Vx2 +5 at x=2? Find the limits by using L.Hopital…

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Q: Calculate the following limits, or explain why they diverge. x2 – 9 lim 1--3 x+3 lim 2x + sin 3x

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Q: 1 lim x→0 x sin x x2 О 14 O 1/7 О 16 O 1/5

A: To find limx → 0 1x sin x - 1x2

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

A:

Q: 1 Prove that lim dx exists and find its value. (1+x?)" 1/2

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Q: lim as x→0 of sin(x4 )/x

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Q: Calculate the limiting value for 1 cos(x*) – 1+5x³ lim x→0 х16

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Q: What is the limit as x approaches 0 of 2x/sin(x)

A: