1 1 4. lim X+0 In(1+x) Arctanx

Q: sin 3x (c) Prove the value of lim Do NOT use L'Hospital's Rule. 0 COS 4x

A: To determine the value of function on the given limit.

Q: 1-cos x 2 Suppose that the inequalities about lim <, hold for values of x close to zero. What…

A: Recall: Limits of function using the squeeze principle:       Assume that functions f, g and h…

Q: p(v) = 4/ 2v2 + 2, a = 1 lim p(v) = lim 4/ 2v2 + 2 v-1 v-1 = 4 lim v-1 lim %3D v-1 4V 2 lim + lim 2…

A: I have used the linearity of limit and limit of a continuous function

Q: sin(ax) e) lim→0 tan(x) f) limr→0 g) limr→ In(x + 1) – In(x)

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Q: lim (1 + sin²x)x X-0

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Q: Indeterminate Form 1 1 6. lim x-0 sin 2x

A: According to Bartelby's guidelines, we can only solve one question at a time, please post again to…

Q: sin 2h sin 3h lim h2

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Q: 8. The graph of y = f(x) has the fc lim f(x) = - 5 lim f(x) = 0 %3D x- - 00 lim f(x) = 0 %3D r- -1-…

A: In this question, the concept of asymptote is applied. Given, limx→∞fx=-5 limx→-∞fx=0 limx→-1-fx=∞…

Q: sin(x?) 48. lim

A: Solution Question 48 Given, limx→0sinx2x We have to find the limit.

Q: Limit tant sec 2t 3t

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Q: sin(a2 – r) + x Secondary Topic 2. Compute lim

A: In order to solve this question you need to know the following notions

Q: lim (e ): + x x→0+

A: In the question it is asked to calculate the result of limx→0+(e3x+x)2x.

Q: lim cot ( x Cannot be determined 1

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Q: 1- sin r 6. Find lim 1/2 CSC x Csc x

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Q: lim x goes to pi/2 at cot x

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

A: wherever an indeterminate form of 0/0 or ∞/∞ exist, we can apply the L'Hospital's Rule. According to…

Q: Proue If lim f(x)=2 and lim g(x)= ) メ→5 メ→5 then lim 2$(x) + (x) - 8 ×ラ

A: Given limx→5fx=2 and limx→5gx=1

Q: 1 1 4. lim X→0 In(1+x) Arctanx

A: 4.

Q: If lim alx) = A and lim b(x)= B then lim alx)-b(x) = A-B メ→C

A: Note: The given question is a multiple question, as per the we are solving the first theorem of the…

Q: Evaluate: lim tan 1+ x +1 1- 3x tanh

A: Given limit is limx→13+tan-1tanhx+11-3x. We have to find the value of the limit, Note that:…

Q: 3. Vx²+3 lim

A: Solve the limit

Q: Evaluate the limit. NOTE: Enter the exact answer. lim x-0 sin? 7x ||

A: Given that: limx→0x2exsin27x

Q: lim (1+ tan 3x)*

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Q: 1 5. lim X→0 xsinx x2

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Q: tan (4x) 3. lim 3x

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Q: Find the limit

A: We will find the limit by substitution

Q: Lim sin?x

A: To Find: limx→01sin2x-1x2 Concept: L-Hopital Rule:limx→cfxgx=00, ±∞±∞, thenlimx→cfxgx=limx→cf'xg'x

Q: sin (x? - 4) 1- V 1- lim 2- lim x1 1-x x2 x - 2

A:

Q: sin (2?- 4a) lim, 4 sin (x2 – 10x + 24) -10x +24)

A: LHospitals rule indeterminate form.

Q: tan 3. lim 2t t→0 ´tan 3x' lim ( ) x→0 csc 3x 5. lim X-0 \3cotx,

A: Topic = Limits

Q: Miscellaneous limits Use the method of your choice to evaluate the following limits.

A: We have to solve the limit: limx, y→0, π21-cos xy4x2y3 We know the formula, cos2 x-sin2 x=cos…

Q: i) lim 5 sin x %3D

A:

Q: Find the limits

A: Consider the given function, limx→∞x2+25-x2-1 rationalize the function,…

Q: tanx (e) lim x-

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Q: 4.) lim x-0 sin 3x 1-cos e 5.) lim X-4 6.) lim x+7- Ix-4|

A: Solutions:

Q: 1. lim- X-0 x2 1-cosx 2.

A: Given,          limx→04x-21-cosx

Q: lim (sin? (x) + sec(x))

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Q: Compute Rn for f (x) = x² on [1,3] and find lim Rn .

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Q: lim 6x2.cot x.csc 2x

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Q: lim Sin(1-Cost) 1- Cast ·

A: limt→0 sin1-cost1-cost

Q: Find lim r0+ sin x 1- sin x 6. Find lim CSc x

A: As per guidelines, I can answer only one question. Since you have asked for multiple, So I did first…

Q: cosh x 2. Find lim. ex

A: We have to find the limit

Q: lim x→→3 x³-7x-6 2x³-11x²+12x+9 ³√x -1 lim X→1 X-1 sina sin 2α lim a-0 1-cos a

A: To evaluate the following limits.i limx→3 x3-7x-62x3-11x2+12x+9ii limx→1 x3-1x-1iii limα→0 sin α sin…

Q: d.) lim f(x) = e.) lim f(x)= -3 -2 f.) lim f(x) = X-I*

A:

Q: Directions: Submit your solution (meaning include all work) to the following question. Please give…

A:

Q: 4. Lim (² x-0 1 Arctanx.

A: Solution Given data  limx→0 (1x-1Arctan(x)) Find-Evaluate the Limit

Q: 4. lim (6x – 3) 5. lim 6. lim 7. lim 8. lim r-1 2-16 9. lim 10. lim(5x - 3x+ 7x + 2)5

A: B)4)limx→-2(6x-3)=6(-2)-3limx→-2(6x-3)=-12-3limx→-2(6x-3)=-15.5)limx→13(x+2)(x+3)=(13+2)(13+3)limx→1…

Q: lim x -> 0  { x(pi/2 - arctanx) } = ?

A: We have limx→af(x)g(x)=limx→af(x)limx→ag(x), so   limx→0xπ2-arctan x=limx→0xlimx→0π2-arctan x.

Q: Evaluate the limit. NOTE: Enter the exact answer. lim x→0 sin? 2x

A:

Q: Evaluate x² –1 lim,→1 -1

A: We know that formula , a2 - b2 = ( a + b ) ( a - b ) Now x2 - 1 = x2 - 12 = ( x + 1) ( x - 1)