domain: vertical asymptotes l:  x= horizontal asymptotes: y=

Q: If f(x) = V19+r² dt , find f'(3).

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Q: Find the interval of convergence of the power series. (Be sure to include a check for convergence at…

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Q: Find the divergence of the vector field F. F(x, y) = 8xe*i – 7x²y²j |

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Q: Question 1 Give an integer a E Z which makes the following equality true for y = x". 7 log.ry (y) 8…

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Q: .W (3) Solve the following differential equations of

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Q: Compute the given improper integral. Enter the exact value of the answ 13 1 dx x² – 25

A: Here we have to find the exact value of ∫5131x2-25dx=?

Q: 4. dr 4-

A: Given: ∫02x34-x2dx

Q: Use double integration to find the area of the plane region enclosed by the given curves. y = 81 – x…

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Q: If 39 | f(z)dz = 7 - 89 and - 39 g(x)dx = 25 89 and 39 | h(x)dæ = 32 89 what does the following…

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Q: 4. Use the definition of integration to find (1+2x' ) dx , that is find lim f(x; )Ax

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Q: Kindly

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Q: Evaluate the indefinite integral. (Use C for the constant of i | sec?(e) tan°(e) de

A: Topic:- integration

Q: Find the limit of s(n) asn → ∞. 64 ( n(n + 1)(2n + 1) n3 s(n) 6

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Q: Evaluate the integral dx (5x + 9)* by making the appropriate substitution: u = dx (5x + 9)*

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Q: dx V1-e2x

A: A detailed solution is given below.

Q: Question 18 Find the length of the curve with the given vector equation. r(t) = (6 + 2t 3) i + (2t…

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Q: | h(r)dr 19 and | h(r)dr = 8.3 what does the following integral equal? h(r)dr =

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Q: Find the indicated limit or state that it does not exist. x2y + xy2 lim (x, y)-(0, 0) x2 + y2 O 2 O…

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Q: Find the equation of the tangent line to the curve g(x) = 5x2 - 6x +2 at the point (1, 1).

A: Use equation of  tangent line

Q: Find T(t) and N(t) at the given poi: x = e cos t, y=e' sin t, z = %3D %3D T(0) = N(0) = %3D

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Q: 1 1 + 25 1 +. 125 Given the series 1+ Does this series converge or diverge? converges O diverges If…

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Q: 6. Evaluate the indefinite integral as an infinite series. (b) / sin z (a) / r cos(r)dr

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Q: dr 2 Vr*+3

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Q: evaluate y" -2y' +5y=0 y(0) =1, y'(0)=3

A: Solve the following

Q: 4. lim (sinx)tanx X0+

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Q: Determine whether the infinite geometric series is convergent or divergent. If it is convergent,…

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Q: Differentiate. 9. y e 10. y- e

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Q: an +1 an +1 an + 1 Recall the Ratio Test which states that, if is a series with nonzero terms, and…

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Q: dx x* +4

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Q: / (3Vi-1)dt is 3 -1 by the 2nd fundamental theorem of Calculus. The derivative with respect to x of…

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Q: f(x) = x-5/x+8 find the domain

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Q: y = 4e2x + xe2x; y" - 2y' + 1 = 0. Yes O No

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Q: 19 Suppose that Ts (x) centered at 2 for f(x) is gien by. Is (X=3+5Cx-2)+8(x-2)²+2G-2)°+(x-2) (3)…

A: T5(x) centered at 2 for f(x) is given by,T5(x)=3+5(x-2)+8(x-2)2+2(x-2)3+(x-2)5

Q: Find ag and a, for the following geometric sequence. 4 4 12, - 4, 3 9 a5 = (Simplify your answer.)…

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Q: Use series to evaluate lim 3x(e -2/x - 1). lim 3x (e -2/* - 1) -O X00 (Simplify your answer.)

A: We can use series to find the limit as below.

Q: Let f(x) : Int dt. Find f'(x).

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Q: Find the distance from the point to the plane. (5,7,6), 10y +z= 0 The distance is

A: We can find the distance as below.

Q: 26) (a) Sketch the region between the given functions (curves): y= 2x and y=x (b) Calculate the area…

A: Given: Curves: y=2x, y=x2

Q: 1 Evaluate dx. - 2x 10 + e 1 dx 2x + C 10 + e

A: To solve the following integral problem

Q: The point P(4, 24) lies on the curve y = z + x +4. If Q is the point (x, x² + x + 4), find the slope…

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Q: For problems 3- 4 determine the angle between the two vectors. 3. p 9i-j, =-37-6j

A: Topic = Vectors As per guidelines , At a time only one question can be answered. please repost for…

Q: -dx is an improper integral. A) True B) False

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Q: 4. If the larger of two numbers is subtracted from six times the smaller, the result is 20. If twice…

A: The detailed solution is given below Thank you

Q: Evaluate the integral below by interpreting y=f(x) it in terms of areas in the figure. A1 The areas…

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Q: 0 1 2. (x + y + 1)dxdy -1 -1

A: Integral

Q: 2) Evaluate the integral S inx dr 2.

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Q: Solve the higher order initial-value problem f''(x) = x-1/x + 3 ; f'(1) = 3, f(1) = 0

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Q: Solve the following differential equations of dy x'y-x'. = y' cos(x). dx

A: Use substitution to reduce the differential equation into linear differential equation.

Q: The derivative with respect to x of | (3Vi-1) dr is 3x – 1 by the 2nd fundamental theorem of…

A: Given that,         ∫3x3t-1dt

Q: 7 Evaluate the sum i(3i + 2) i=1

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