State where the power series is centered. (-1)"(2n – 1) „n Σ * 2"n! n = 1

Q: Solve  x * (dy/dx) – x6ex = 4y

A: on solving this we will get :-

Q: y = x(x2 – 4)

A: We have to find the area of the shaded region.

Q: 10 %3D1

A: Formula Given

Q: 3 roblem 4. The third term of a geometric sequence is 9, and the common ratio is Find the fifth…

A: Given problem:- The third term of a geometric sequence is 9, and the common ratio is 3/2   Find the…

Q: completely

A: We will solve the integration.

Q: iF Zz fexiy) where R= ě- ě Gud ge ě- ě show That!- +y5= (e-ぎ)( - 24

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Q: d Calculate ri(t) · r2(t)] and ri(t) x r2(t)] first by differentiating d dt' the product directly…

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Q: Differentiate the following using implicit differentiation 3/a + V = 7

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Q: Find div F and curl F if F(x, y, z) = 9e"Y i – 2 cos yj+ 7 sin? z k. div F= curl F=

A:

Q: A ball is thrown into the air and its position is given by h(t) = - 4.3t2 + 41t + 15 where h is the…

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Q: ||r(t) × r"(t)|| ||r(t)||³ Use the formula k(t) = to find k(t). r(t) = 4 cos(7t)i + 4 sin(7t)j + 3tk…

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Q: X1 + 2x2 + x3 = 12 X1 – 2x2 + x3 = 0 X1 + x2 – x3 = -1 Solve the following system using Gauss-…

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Q: Find the sum of the series. s 7(-1)"72n + 2n + 1(2n + 1)! 00 Σ n = 0

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Q: In which limits below can we use L'Hospital's Rule? x – 2 lim 1→2 In(3 – æ) 1- et lim 2-0 sin(5x)…

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Q: (a) Find the value of P(?, 4) and P(?, 6) using permutation formula, where ? is the last two digits…

A: Permutation: Permutation:  The permutation is a method of arranging objects in a specific order.…

Q: Find the value of the series: 1+2" 3n-1

A: We have to find sum of series.

Q: Find r'(t). r(t) = (tan-(7t))i+t cos(t)j – Vēk

A:

Q: Determine the convergence or divergence of the series. (If you need to use

A: answer is in next step

Q: Find div F and curl F if F(x, y, z) = xz³i+ 4y°x²j+ 6z²yk. div F= curl F =

A:

Q: 9) use the snell metnod to sef up end eveluete tueinteyrel tret gives the volume of the solid…

A: Using shell method, volume is evaluated.

Q: SUTM i) Find the domain 1. Given z = f(x, y) = /36 – 9x² – y-. of the function. ii) 3 UTMd rano UTM…

A: Let's find.

Q: S-2 ds (s-1)(s-5)(s+3)

A:

Q: ; Test the following series whether it is convergent or divergent (show all your works) n2 +7 a) 2…

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Q: 1. S 2x-6 すdx (x-7)5

A: Solution:

Q: 2. S x²-6x-4 xp x+2

A: Given: I=∫x3-6x-4x+2dx As we know that; The Power rule: ∫xndx=xn+1n+1+C And ∫a·fxdx=a·∫fxdx

Q: Find div F and curl F if F(x, y, z) = xz°i +2y°xj+62

A: Given: Fx,y,z=xz6i+2y8x2j+6z2yk

Q: Find a basis for the eigerspaca conesponding to the eigenvalue 12. 17 141 12 A basis for the…

A: We want to find the basis.

Q: Find two other pairs of polar coordinates of the given polar coordinate, one with r>0 and one with r…

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Q: Use a Maclaurin series in this table to obtain the Maclaurin series for the given function. f(x) =…

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Q: Consider the system of differential equation x' = 5x – 3y - y' = 9x + 9y Write the system in matrix…

A: To find the matrix A.

Q: 3) use implict differentiation to finol dd et the point (8.1). 4 xy+ slny=32 Anywery: 28 a) 37 り 36…

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Q: In(x) -dr

A:

Q: t3 – 7t2 + 16t –- 12 t4 – 4t3 + 4t² 5. lim t2 w? – 4w + 1 6. lim w-00 3w2 + 7w – 4

A: limt→2t3-7t2+16t-12t4-4t3+4t2

Q: e cosx sin x dx 1-e2 cosx

A: Given problem:-

Q: Find the area lying outside r = 6 cos 0 and inside r = 3+3 cos 0. Area =

A:

Q: 2.2 State the identity that validate sin x = 3 cos x- and hence show that 6+9/3 tan x = [10] 23

A: Follow the procedure given below.

Q: Determine the area of the glven reglon. y = x + sin x 3- 2- Step 1 Note that for the given reglon, x…

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Q: x+1 8. -dx (x-1)

A: As per rule of bartleby we can solve only one question at a time and we can solve only three subpart…

Q: Find the domain of r(t) and the value of r(to). NOTE: Round your answer to two decimal places when…

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Q: (-2,0,5) and (–1,2, 3). Find an equation of the sphere whose endpoints of a diameter are

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Q: Find div F and curl F if F(r, y, z) = xz°i+ 2y°x²j+ 6z²yk div F= 2° + 16 y' x + 12 z Y curl F=

A: Given F(x,y,z)=xz6i+2y8x2j+6z2ykTo find div F & curl F:

Q: Graph the problem and solve using vertical or horizontal rectangle. Show your solution. 1. Find the…

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Q: Let A + 0 and ACB. Show that NB CNA.

A: Given :A≠∅A ⊆ B

Q: V3x - 2 lim tan- %3D x + V3

A:

Q: Evaluate the limit 5+ 9x lim 1+00 3 – 4x

A: Given problem:-

Q: 7. Find the linear approximation near (2, 0) of f(x, y) = 3x e¯3ªy.

A: To find the linear approximation for the given function.

Q: Find V. (V × F), if F(x, y, z) = 3e²*i+9xe*j – 4ev*k V· (V × F) =|

A: Use the curl and divergence for the F.

Q: The radius of a circle is increasing at a rate of 5 centimeters per minute. Find the rate of change…

A: We can find the answer as below using the given data.

Q: Find the general solution of the given variable separable egm atim. dy *+ ay? (2) %3D

A: Given :dydx=e3x2+4y2

Q: 3. If z = f (x, y), where x = e“ – e® and y = e® – e", show that UTM UTM az az UTM X : az - ду dx…

A: