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 x

Q: Evaluate the limit using L 'Hospital's rule: lim x to 0 e^x -1/sin(12x)

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Q: Tim (X-1)sec(Tix/z) X -

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Q: Determine the following limits analytically.

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Q: Find the limit by interpreting the expression as an appropriate derivative. In(e + Ax) – 7 (а) lim…

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

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Q: Use L'H to find the limit at x \arrow 0: arctan(5x)/x   x-->0

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Q: use l’Hôpital’s Rule to evaluate the limit

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Q: 2) Use the definition of the definite integral to write 2 e* dx as a limit. Do not evaluate this…

A: In this we use the limit  definition of definite integral

Q: lim, (5 イータ 1-Sint Cos C)

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Q: Evaluate the following limits (if exist): 1-cos(ax) (c) lim- a+0 (d) lim/Vxr'+x-Vx°-cx), where c is…

A: To evaluate the given limit we are using L- Hospital rule

Q: Express the limit as a definite integral. n 7 lim 8 1 + i = 1 n- o n dx

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Q: Find the limit of the given functions using a numerical approach 3. lim (2 cos x) 3T 4.

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

Q: To apply the divergence test for ,3/n² n=1 we need to evaluate lim e3ln? n→∞ What is the value of…

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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…

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Q: Express the limit as a definite integral on the given interval. lim n - 00 cos(x}) Дх, [2л, 5л] Xi i…

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Q: ) Use L'Hôpital's Rule to compute the limit lim (e* +x)/=.

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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: what is the limit of (cos(x))^4/x^2 as x approaches 0 from the positive side?

A: Given,

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: 2. Compute xe" da using a limit.

A: The given which we have to find the integration from 0 to ♾️  f(x) = xex

Q: Express the limit as a definite integral on the giveninterval.

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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: Determine the value of the following limit and show that it exists. x² tan (x) lim (1,y)→(0,0) x2 +…

A: Limit exists and limit value is 0.

Q: Use l'Hôpital's Rule to find the limit. lim 0-0 4-4 cos 0 sin 20 OA. 2 О в. о OC. ∞ OD. 1

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Q: Compute the limit as xà0 of f(x)=(sin(61x))/x, if possible.

A: To find:limx→ 0sin61xx

Q: Evaluate the given limit. Show your complete solution. limo(-x ln(sin(4x² + x)))

A: The given limit is limx→0-xlnsin4x2+x. We have to solve the limit using L'Hpotial's rule.

Q: lim h→0 (e) cos( 4 + h) - 1 h

A: To find the limit of following function

Q: Evaluate the​ limit, where a and b are constants with b≠0. lim x -0 sin ax/ sin bx

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Q: e* + e * — х2 — 2 lim —х sin?x – x2

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Q: Use​ l'Hôpital's rule to find the limit of limθ→0     7 cosθ−7/2θ.

A: Given limit is in the 0/0 form so we can use the L'Hôpital's rule

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

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Q: What is the limit as t goes to 0 of    4 tan^-1(t)

A: Topic:- limit

Q: Find the limit by interpreting the expression as an appropriate derivative. In (e10 + Дӕ) — 10 (а)…

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Q: Find the value of a for which the limit sin (ax) – sin x – x lim x→0 is finite and evaluate the…

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Q: Find the limit as x approaches 0  2sin23x/3x2

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Q: The following limit represents the derivative of a functionf at a point a. 5 tan 6. V3 f '(a) = =…

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Q: Prove: the limit as x approaches 0 1-cos(x)/x=0

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Q: Evaluate the following limits by constructing their respective table of values. 1- cos(3t) 4. lim 3t…

A: note: as per our company guidelines, we are supposed to answer 3 sub parts of a given question.…

Q: Express the following limit as a definite integral: lim 2

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

A: Given, limx→01x sinx-1x2

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: 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: 11) lim sin²y Y→TT 1+cosy

A: sin2y=1-cos2ya2-b2=(a+b)(a-b)

Q: To apply the divergence test for Σ „5/4n² n=1 we need to evaluate lim eS/4n?. n→∞ What is the value…

A: Here we have to find the value of the limit.

Q: Express the limit as a definite integral on the given interval. lim x, In(2 + x^)Ax, [3, 4] n- 00

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Q: By using the de finitionof the limit, prove thal (D Lim x (x+1)=D0 e) Linx cos= o

A: Let f(x) be a function defined in the open interval a,b and let c be a point in the interval a,b…

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

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Q: if r =-1 A if z + -1 2. Is f(r) = continuous at r =-1? (Show your work using limits.)

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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.