2. Find the exact limit. Assume a is a constant. SHOW WORK!!! sin(nx) sin(ax) lim 3x2

Q: Find the limit of sin(6x) limy→0° sin(2x)

A:

Q: Verify that L’Hôpital’s Rule applies and evaluate the limit.

A:

Q: Evaluate the limit. (If an answer does not exist, enter DNE.) sin(8x) – 8x cos(8x) 8х — sin(8x) -…

A: Since the given limit is in the indeterminate form of type 0/0 , therefore we can apply L'Hopital's…

Q: Find the limits x2/3 + x1 lim X00 x2/3 + cos?x

A: Given: The function is f(x)=x2/3+x-1x2/3+cos2x   To determine: limx→∞ x2/3+x-1x2/3+cos2x

Q: Verify that L’Hôpital’s Rule applies and evaluate the limit.

A:

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

A:

Q: Find the limit. sinx cos 4x lim x-0 x + x cos 5x 4 A) 을 B) 0 530 C) D) Does not exist

A:

Q: 4) Find the following limit or show that it does not exist. sin(ry) a) lim (1,y) (0,2) b) lim…

A:

Q: Compute the following limits sin5x (1) lim- x→0 sin10x

A: We have to find Limit of given rational function using L'Hospital Rule of (0/0 form).

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

A: Given: u=(1+sin(3x))1x We want to find  limx→0+u=limx→0+(1+sin(3x))1x Since we know that u=eln(u)…

Q: lim 4 x→0 2 1 +sin (2) cos sin

A:

Q: lim 4 sin(x + n) + 3

A:

Q: x cos(2x) (c) lim x-0 sin(-3x)

A:

Q: Evaluate the limit: lim sin(2x) cos(7x)

A: To evaluate: limx→0sin2xcos7xx

Q: 2x sin-x lim х—0 еx — Х — 1

A:

Q: By whatever justifiable means, find In(1 – 22) lim sinh z e – In(e – z) - and lim z+0 z – 1+cosh z |

A: To evaluate the given limits

Q: Find the limits lim x→ -1+ cos-1x

A: We find the limit by substitution

Q: Find the limit.

A: Given- x→lim0 sin3xx To find- the value of the above limit. Formula used- Using the standard form as…

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

A:

Q: Determine the following limits analytically.

A: limx→0  3tanx - 8x3x + sin2xlimit = ?

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

A:

Q: Find the limit, if it exists

A:

Q: Evaluate the limits sin3h-2h 4) lim sin?x 5) lim x 0 1-cos x

A: (4) limh→0sin3h-2hh=sin3(0)-2(0)0=00=indeterminate form Apply L'Hospital rule,…

Q: Find the limit. lim sin(ax) . x-0 sin(9x)

A: If we plug x=0 in the limit then we get:

Q: Find the limit, if it exists. lim X 00 4X + sin x 2.

A: Our aim is to find the limit of the following:limx→∞  24x+sinx  = ?

Q: Estimate the limit numerically or state that the limit does not exist (DNE): lim x→0 sin(11x)/x

A: Evaluating the limit

Q: cosx * sin? (3x) 2 2. lim x→0 x2

A:

Q: Compute the indicated limits. sin(2x) lim 3x

A:

Q: 2. Calculate the following limits: (a) COS x – 1 lim x40 sin x In(1 + x)

A: To find the limit Lim(x tends to 0) [cosx-1]/sinxln(1+x)

Q: What is the value of a if the limit of the function is 3, given by еах —1-ах lim X→0 ex2. = 3? -cos…

A:

Q: Use l'Hôpital's Rule to find the following limit. 3 sin (x) – 3x lim 4x3 3 sin (x) – 3x lim (Type an…

A: I am going to solve the given problem by using some simple calculus to get the required result.

Q: Calculate the following limit: lim(1x)4 sin(13a x→0

A:

Q: Find the limit using L'Hospital's Rule. e 2x – 1 lim x→0 sin x

A: We use L hospital's Rule

Q: Use continuity to evaluate lim sin(2x + sin 3x) Enter I for o, -I for –o, and DNE if the limit does…

A:

Q: x sinh x 1. lim x0 cos 3x -1

A: The solution of the problem is given in the next step.

Q: Find the following limit limx→0 (1/sin x − 1/x)

A: limx→01sinx-1x=limx→0x-sinxx·sinx=0-sin00×sin0=00

Q: 2 cos(4x) – 4x² – 2 4. lim х-о sin(2x) —х2 — 2х

A:

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

A:

Q: Estimate the limit numerically or state that the limit does not exist (DNE): sin(9x) lim x →0

A: Please refer the attached image for complete solution. THANK YOU.

Q: Find the limit. lim ey sin P -(5, 0, -5) O 1

A:

Q: (b) lim log1 r+2+ (x – 2)? sin(2x2 – 3x – 2),

A: solution:-limx→2+ log13x-22sin2x2-3x-2=limx→2+ -log3x-22sin2x2-3x-2=limx→2+…

Q: Find the limit 1- sin z In (100r² + e*) (a) lim (b) lim 1+ cos 2r 100z

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Q: Find the limit. lim sin-2x i

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Q: Q.3/ Find the limits for the following: 1) lim sin 7x 2) lim x0 sin 5x 3) lim V-3 x→9 ズ-9 x1x3-

A: We will find the limit.

Q: 2. Find the limit using Squeeze theorem 1 lim,2|a – 2| sin( `x – 2

A: Given: limx→2x-2sin1x-2

Q: Compute the limit below. Justify your answer. sin(24x) lim- 39x

A:

Q: Estimate the limit numerically or state that the limit does not exist (DNE): sin(7x) lim x →0

A: Given:

Q: Find the limit. tan(12t) lim t-0 sin(4t)

A:

Q: calculate the limit.

A:

Limits

When it comes to calculus, limits are considered to be a very important topic of discussion. The main importance of limit lies in expressing the value of a function as it gets closer to a certain value. Also, limits can help you to understand other topics, such as continuity and differentiability better. In a broader sense, every calculus notion is a limit. Other branches of calculus have also been derived from limits.