53. Show, for f(x) = 3x2 + 4x over [0, 2], that ( 12j², 8j Σ%) RN N2 Then evaluate lim RN.

Q: Evaluate the following by limit of su (3x² +5)åx (sin x)dx

A: Solution:To find the integration Formula:∫xndx=xn+1n+1+Csin2x=1-cos 2x2∫cos ax=sin axa+C

Q: Juneten and be fure at lebel aut least thre f (n) : Su

A: As asked we can find the answer as below

Q: Compute the following limit: 1-cos 2z 1. lim I→0 z sin 2x· Hint: 1 – cost = 2 sin? t.

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Q: 5. If b > 0, prove that lim = 0. %3D 1+nb

A: as per our guidelines we are supposed to answer?️ only one question. Kindly repost other question as…

Q: b) Given f(x) = V5x + 1 , Find lim x+h)-s(x) ,when x > %3D h-0

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Q: b* – 1 Show numerically that for b = 3 and b = 5, lim аppears to equal In 3 and In 5, respectively.

A: Given : limx→0bx−1x

Q: 3. Show that the largest value of o that can be used for some e > 0 if lim (2+ 5x) = 17 is エ→3 anx"…

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Q: 43()3De"fur all regl numbras x.find Lim g D4-ズ

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Q: Suppose the inequality (x² – 4x + 3) < f (x) < cos ( TX *) holds for all values of x. 2 Find lim f(…

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Q: sin2z+7z2±2z 4. lim X-2 z2 (z+1)2

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Q: What is (ro s)(x), if r(x) = V2x – 4 and s(x) = x + 2x? O a. V2x- + 4x – 4 | O b. V2x2 + 4x - 4 O…

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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: 2.14 Show anx" + ... a12 + ao lim n an bn .. provided that b, # 0.

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Q: Show: ( (|fl2 – €)² < lim sup E If (n) < (I|fl2 + e)² , Where ƒ E C(R | Z; , c) n=-N

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Q: Express the limit as a definite in 7 lim 1 + (i/n)3 n→ 0 n i = 1 1 7n dx 8

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Q: 2² + e4 z lim z 0 22 – e²

A: This is a form of infinity by infinity so we have to apply Lhospital rule that is differentiate both…

Q: (a) Determine the following limits without using L'Hôpital's rule. V7x° +4x -x² -2 lim x'-2x-3x+1…

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Q: Find the limit. 5xz - 7xy P (1, - 1, 0) x2 + y2 - z2 lim %3D O 5 7/2

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Q: What is the limit as x goes to 0 for (e^x-1-x)/x^2?

A: Please refer the attached image for complete solution.

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: Ql(i) Prove that Lim t* ... /2n²+1 2n²+n]

A: The series is Lim12n2+1+12n2+2+......+12n2+n=12

Q: Show that for any &> 0 and Sn = 1X₁, lim P(|S₁ − 0| ≥ ɛ) = 0. n-00

A: We will use Chebychev's inequality to find the limit of given probability.

Q: Show that Hint: Use to obtain In[|x|] √√2/T. 1 - cos(sx) x² 8 1 - cos" x x² lim n-√√n 00 2 π dx |s|…

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Q: 2/3 Determine the length of x=| for 0<ys2. Assume that y is positive.

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Q: He sold his stock when t = 4. Compute the following (if it does not exist write DNE): Lim-4- J(t) =|…

A: Given,

Q: (a) ' Compute the following limits 7x3-5x+1 (i). limr→0 4p3+a²+x-8* (ii). lim,0 V5x+1–1 5x (iii).…

A: a) limx→∞7x3-5x+19x3+x2+x-8= limx→∞x37-5x2+1x3x34+1x+1x2-8x3limx→∞7-5x2+1x34+1x+1x2-8x3=…

Q: For z + y, lim ()(1,1) Va - A. 0 В. 2 C.1 D. Does not exist.

A: This is simple question can be solve by rationalising the given function Solution is given below

Q: y om U to 1.0 how can you find limits bntegroutlon.

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Q: |Suppose that dy = y3 + y? – 9y – 9 dx %3D and that the point (13, –2) lies on the graph of (x, y).…

A: Given:dydx=y3+y2-9y-913,-2 lies on the graphTo find limx→-∞y

Q: Show that for any e > 0 and S, 1X₁, lim P(|S₁-81 ≥ 2) = 0. y'a 3140

A: We will use Chebychev's inequality to find the required limit of probability.

Q: Q3 (A): By using "L' Hopital rales "; Find the limits of: (1) limal; (2) Itm X(tan-¹x-x)

A: I have solved step by step in detail...go through the solution

Q: 5. Show that x³y³ lim (x,y) →(0,0) 2x¹2 + 3y4 does not exist.

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Q: Show that when T(z) = az+b cz+d where (ad - bc ‡ 0), find lim T(z) = ∞ if c = 0. 7-3

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Q: e n Show that for any &> 0 and S, ₁X₁, lim P(S₁-0 ≥ 8) = 0. =

A: We will use Chebychev's inequality to find the required limit of probability.

Q: 9 Give with an not example of T: W≤X →Y, to XT Ext. .R. boundedag. - keše bes

A: Please find the solution innext step this is an non-example of Tietze extension theorem in Topology.

Q: Along the path x = e find lim (1,y)→(1,0) y2-6ry 3x-y-3 O 2 O does not exist O -3 O 3

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Q: 4) If y = (x² + 1)cos(3x), then find dy/dx. 5) Evaluate the following limit e cosx – 1 lim x-n/2 2x…

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Q: Let fa)=S(-5-x2 + 23x +19 f Xチー6 if X= -6 calculate the following limits. ENter DNE if the liniit…

A: l

Q: The limit fx= X2 XスT 2メ-ズ Cos X ,X < TI at Will be 1-itexisted and eanals T 2-It existed and equals…

A: In the question we have to find correct option.

Q: Q2: Evaluate: 2 In cosy, [1] limy-o [; y4

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

Q: S (2t)*dt lim x→ =? х* — 1

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Q: 2 let fcx)=メミメ6, fiad X +2 a) limfcx) Xー72 bllim fcx) メー70 c) lim fex) メーフ3

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Q: What is the net crarop for fW={+5,05 as we qo from x=2 to X=5?

A: The given function  f(x) = x2 + 5

Q: Evaluate the following limits by constructing the table of values. 1. lim -cos(3t) 3t t--0 f(t).…

A: Note:- Since you have asked multiple question As per our policy, we will solve the first question…

Q: 2. Let x E (0, 1), use e – d to prove V4 +x – 2 lim 1 4

A: 2. Given x∈0,1, limx→04+x-2x=14                       ... (1) Use ε-δ definition to prove above the…

Q: Find the limit of f(x) = as x approaches co and as x approaches - oo. 4 -

A: Given,          fx=-4+2x4-6x

Q: 5-Vx+25 limr→0

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Q: 1-e X x2 +1 X By using the limit comparison test, the integral

A: Using, limit comparison test

Q: 5) why is x3- 3x +I X +2 Conti nuous (0,00) on where is it discontinuous?

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Q: Find the limit of (x3+x2)1/2sin(((2)1/2pi)/x) as x approaches 0

A: To find