41–46. Limits Evaluate the following limits. sin t sin e' – t - cos t + t²/2 – 1, 45. lim

Q: |Find the limits. Enter "DNE" if the limit does not exist. 1- cos(5xy) lim (1,9)→(0,0) xy lim…

A: We have to use proper substitute for the first part.

Q: Find the limit, if it exists.

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

Q: sin t t8 lim sint t→0 +3

A: NOTE*** As per bartleby guidelines for more than one question asked, only first to be answered send…

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

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

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Q: 2. Find the limits. limx→-1 sin(x² + 3x + 2) x³ + 1 M

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Q: Find the limit. y sin x limx.y)(0,1) O 1 8. O No Limit

A: Find the limit. lim (x.y)→(0,1) (y5 sin x)/x To select correct option  1 0 ∞ No Limit

Q: Q3 :(A): By using "L' Hopital rules"; Find the limits of : 1 (1) lim,-ol1-cos x sin2x (2) lim,…

A: 3)1) limx-0[1/(1-cosx) -2/sin2x ] 2) limx-0(tan-1x-x) /x3 Repost the next question.

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

A: 3 1) limx-0[1/(1-cosx) -2/sin2x ] 2) limx-0 (tan-1x-x) x-3

Q: sin(In r) 5. Use the Squeeze Theorem to evaluate lim 1-40+ In (sin z)*

A: Solution is given below:

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

A:

Q: Q3: (a) Find the following limits if exist (without using L'Hopital's rule):- (2) lim,- tan r-sinx…

A: Explanation of the answer is as follows

Q: Evaluate the limit. –1+}² 1.2 COS I lim 2.x4

A:

Q: Q3: (a) Find the following limits if exist (without using L'Hopital's rule):- (2) lim, (3) lim,…

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Q: evauluate the limit lim x→0 (sin2 (3x))/ x2

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Q: Find the limit, if it exists: 1 lim (7,y) → (0,0,0) 6 tan x² + y² + z² (Give the answer in exact…

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Q: Q2: (a) By using " L' Hopital rules "; Find the limits of ::- (1) limx¬(n/2)-(tan x)cos x (2) limx-o…

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Q: sin xy lim 0.

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Q: The value of limit x→0 of {sin (a + x) – sin (a – x)}/x is

A: we have to find the value of  limx→0sin(a+x)-sin(a-x)x

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

A:

Q: Calculate the limit for the function f(x) = Ex + 4 over the interval [0, 4]. Verify your answer by…

A: Given the function

Q: 1. Express the limit as a definite integral on the given interval. Xi lim Ax, [1, 3] '(x;)² +13 n00

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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 limits [ sin(3t) lim Li+ In(sin(3t)) j+tln(3t) k sin(t) In(tan(t)) t+0

A: Since you have asked multiple questions in a single request so we will be answering only first…

Q: II. Evaluate the limits. tan 0 2. lim 0 -0 sin 20 (y-#)* 2. 4. lim t 1-sin y y - 2 2.

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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: Find the two limits: sin 2x lim r-T/2 COS x

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Q: Find the limit. sin(x – 3) lim х>3 x* + 5х — 24

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Q: 5 sin(2z) z-40 1- cos(2) Find the limit. lim COS

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Q: Q2: (a) By using " L' Hopital rules "; Find the limits of ::- (1) lim,-(n/2)-(tan x)cosx (2) lim,--0…

A: L'Hôpital's rule states that for functions fx and gx which are differentiable on an open interval I…

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. lim est - 1 t-0 sin(t)

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Q: Find the limit. lim vx+11 cos (x + 3T) X-- 3T lim vx+11 cos (x + 3r) = →-3T Type an exact answer,…

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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: Find the limit. x² + y® sin х - у +7 lim (x.y)→(0,0)

A: Given,

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

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: I. Evaluate the following limits: sinh(x2−x2) 1. lim x→0 sinh(x−x) 2. lim (x - ln x)* x+0+

A: The given problem is to evaluate the given limits of the given functions by checking the left hand…

Q: a)Express the limit as a definite integral. Σ (3c-5)Ax, xe[0,1] lim 2 b) and then evaluate it.

A: lim∆→0∑i=1n3c2i-5∆xi  x∈[0,1]∑ =∫∆xi=dx∫01(3x2-5)dxThis is definite integral

Q: Evaluate sin(x – 3) - lim x→3 x2 + 1x – 12 Limit = (Enter DNE if the limit doesn't exist)

A:

Q: Find the limit or prove that it does not exist lim (2,y)→(0,0) T° cos x + 2y sin y x2 + 4y2

A: We will evaluate the limit limx, y→0, 0x3cos x+2y3sin yx2+4y2  using polar coordinates.

Q: f(x) lim sin(5x) X I 0 -0.25 3 2 Estimate the limit numerically or state that the limit does not…

A: We have to find out limit

Q: Find the limit

A:

Q: I. Evaluate the following limits. x sinh x 1. lim x-0 cos 3x -1

A: Since you have asked multiple questions, as per Bartleby guideline, we are allowed to answer only…

Q: lim (x.y)>(0,0) 2x sin y 2x +y Use the &- d definition of the limit to prove that

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Q: Evaluate the limit sin 2x lim z+0 9x

A: Answer and explanation is given below

Q: Evaluate the limit sin 7h lim %3D 7h Enter DNE if the limit does not exist. Limit =

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

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Q: -x + 1, x > 0 3) Let f(x) = sin x -,x < 0' (a) Find left-hand and right-hand limits as "x"…

A: we have given f(x).  We have to find the left hand and right hand  limit.

Q: 3. Show that the function | sin(2.x)| is not differentiable at r = 0 but the function | sin(2x)|1+T…

A:

Domain

In simple mathematics terms, a domain is defined as the space on which all the possible inputs for the function will lie. It can also be expressed as a set of departures for the required function.