N 3s2 – 4s – 4 lim V→∞ s=1 N³

Q: x sin(2x) 1- cos(x) limr→0 | А. О В. 1 С. 2 D. 4 E. the limit does not exist ||

A: The given expression is limx→0xsin2x1-cosx. Evaluate the limit limx→0xsin2x1-cosx as shown below.

Q: (2 cosh z, sinh z, 2 0. Then the lim f(x) A does not exist B is 2 C is 1 D is 0 B

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Q: Prove that

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Q: C. Find the following limits: 1) limy-o 2ytan(n/y) sin(n-02) 2) limo2→n Tøl-V

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Q: Let y(t) denote the solution of the given initial value problem. Is it possible for the…

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Q: Using the Nth term test for divergence, V5n-2 n2 n=1 diverges since lim V5n-2 n² is equal to n→∞ 8.

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Q: Find lim (x,y)→(12,3) xy cos(x – 4y). OS 1. –36 2. 36 3. 3 4. 0

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Q: 2.r + y Find lim (x,y)→(0,0) 2.x²y + xy² or show that it does not exist.

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Q: 8. Which of the following limits is equal to x* dx? (A) lim E 3+ n) n k2 (B) lim 3+ n) n k=1 2k* 1…

A: Explained below

Q: Along the path z= e find 2. lim (2,4)→(1,0) y-4zy 3x-y-3

A: Here, we have to reduce this limit to a limit in a single variable by using the equation of curve.…

Q: Q4 / Vx+1–1 A ) Find limx→0

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Q: 8. Calculate the following limits. 3 + 4x² + 2y? xy – 2x – y + 2 (a) lim 2x2 + y? (b) lim…

A: (a) Limit does not exist. (b) The limit is zero.

Q: Find the limit. 7e - 7 V1 + t - 1 9. lim t t 1 + t

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Q: Q3// Evaluate (a) lim,4 VE-2 S-V49 sin 3y cot 5y (b) limy-o y cot 4y

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Q: t² + 1 t 1 %3D lim→1- h(t) = ?

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Q: Let y(t) be a solution of ý = y(1 – ) such that y(0) = 6. Determine lim y(t) without finding y(1)…

A: Now,

Q: (t + At)2 – 7(t + At) + 3 – (t2 – 7t + 3) lim At0 At

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Q: Choose the correct answer for the following limit Q1_V1_M S sin t3 dt lim x-0 1 2 x4 (A) 3. (B) -1 3…

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Q: |8x – 1|+ 2 (b) lim T→士o 7 – 4.x Hint: you will have to consider the limits at oo and at —00…

A: To calculate: limx→±∞ 8x-1+27-4x   Now, limx→∞ 8x-1+27-4x 8x-1 is positive when x→∞.  Therefore…

Q: Q. 2 Find the following limits v' -8 a) lim v* –16 v+ 2 4x –x 2- Vx b) lim 4

A: The limit of a function is the value of the function at which the arguement for the function tends…

Q: 8r + 5tant Find lim t>0 sint

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Q: 3 of 20 Select the best answer. (2e + 1)ª lim z+00 (tan(x))- O DNE

A: We have to find the limit.

Q: 3. Show that lim(r.y)→(0,0) xy =0. (Hint: Use the fact the y| = Vy² and therefore y|< Vx² + y²)

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Q: lim, „(Væ² + x – x)=? O a. 0 O b. 1 O c. Limit does not exist O d. 00 O e. 1/2

A: In these type of questions just rationalize the given term and simplify the fraction before finding…

Q: D D ▷ TEXA fex) (2k- x 1 Fx k evaluate lim Can you choose Parameter k proper value for k x21 x < 1 a…

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Q: Sirlw)dk= f (x) κ= lim Σ fx%) Δx 25.) Use the definition, -2x n+00 i=1 to evaluate Σ Ei=" (n+1) Eř="…

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Q: Vx + 32 - 5 Limit. lim x--7 X + 7 O 0.1 O Does Not Exist (DNE or tco) O 10 O 1.4 O 5

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Q: (3 + 5y +7{ ) 2+y? 200 + y02 exists if lim r)(0.0)

A: This is a problem of multi variable calculus.

Q: Q3 Find the area inside one leaf of the three leaved rose r-cos30 (upper lim and lower limit= n/6)

A: Given: The value of r and the value of θ. To find: Area inside of 1 loop. As per policy guidelines,…

Q: 7. Find the limit as x approaches 0. F V I 2 2 O infinity O limit does not exist Oo .

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Q: Can i get help with this problem step by step?

A: Here, we rationalize the denominator to get the required value of limit.

Q: Which of the following is not true? 4dx 4dx A S.. lim √x(x+6) c √x(x+6) 5 dx dx So 25-x² B = lim…

A: We have to find out the option

Q: 23. lim Vx2 + y² In(x² + y²) (xy)→(0,0)

A: This question is related to limit in two variables.

Q: i) The area of the surface obtained by the rotating the curve y=V 16-x², –1s×s1 about the x-axis is…

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Q: (4x 5y) (z,y)→(1,1) 5x2- 7y lim O 1/2 O 1/2 O Limit DNE

A: We need to evaluate the following limit limx,y→1,14x-5y5x2-7y

Q: Find the limit. 1 t1 5 lim 4e 4 1t t 0 t t LC

A: First we take the limit inside and simplify

Q: Using the Nth term test for divergence, 00 n 5n-2 n2 n=1 diverges since lim V5n-2 n² is equal to O 5…

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Q: (4x – 5y) lim (x,y)→(1,1) 5x² – 7y O -1/2 O 1/2 Limit DNE

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Q: -1 sx3 O A) -0 O B) -1 O C) 7 O D) Does not exist

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Q: 8 lim r→8 r2 8x Enter DNE if the limit does not exist. Limit =

A: Given limit:

Q: Find lim r(t) when 5 In t r(t) = (: 2 tan¬lt, e-2 t 2 tan-t, e 1. limit = (2т, —2, 0)

A: Given    r(t) = 2tan-1t , e-2t , 5 lnttwe need to  find  the limt→∞ r(t)=?

Q: If y = y(x) is a solution of y + 5y = 3e-2x + 3. Find lim y(x). x00 3 7 b) O Does not exist. 2 3 f)…

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Q: 'e in + = "T 2n Find lim a

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Q: 2t – 2 t2- 1, Let r(t) = - î - tan (t) ĵ+ In(2t) k. %3D (a) Determine the domain of r. (b) Compute…

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Q: {fn(x)} = {n²x(1 – x)"} for æ € R and n = 1, 2, 3.... | 1.find pointwise Limit

A: The given function is, fn(x)=n2x(1-x)n

Q: Ex let yct) soluton to the I.V.P y"-y'-2oy=0, yco) =3 , yto) = b If . Lim yL)= O find b?

A: Explanation of the answer is as follows

Q: (x + x)T 3 - x) dx = lim n- 0o n If where a, B and y are positive integers, then a + B +y = зо 20 16…

A: Given, ∫-21x2+xdx Here, a=-2 and b=1 We know that, ∆x=b-an=1--2n=3n and xi=a+i∆x

Q: 2x Sí“(2t-2)² dt (a) Find the limit (if exist): lim 1 2х-1

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