Sketch the region bounded by the graphs of the following functions and find the area of the region. y = x² – 1, y = -x + 2, x = -1, x = 1

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: 2. Find the r educed echelon form of the fo A = 0 0 0 6 54 0 (714161 Show your working

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Q: 4. Show that y=e²* sin 3x satisfies the equation: y" – 4y' + 13y = 0 %3D

A: Topic = Differential equation

Q: v F= F=

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Q: Determine the vector field of F. F(x, y) = 6i – 3j

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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: sec(Inx) tan(Inx) dx

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Q: 8 Evelluate the double integral: + 3x) dydx

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Q: View Policies Current Attempt in Progress Find r'(t). r(t) = (tan-(9t))i+t cos(t)j – Vik | NOTE:…

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Q: `x² In x dx

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Q: Verify that the conclusion of Clairaut's theorem holds, that is, u, Uxy = "yx' u = x'y8 – y? With u…

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Q: Calculate the power series solution of the differential equation of y'- y= e* up to the five terms.…

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Q: dx 9- x 15.

A: Topic = Integration As per guidelines , At  a time only one question can be answered out of…

Q: Given the function g(x) = 4x° – 36x?+ 96x, find the first derivative, g'(x). g'(x) = (x),6 Notice…

A: Given that, the function is g(x) = 4x³ - 36x² + 96x We have to find the g'(x),g"(x) and have to…

Q: 15 dy dt 2-

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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: Find V· (V × F), if F(x, y, z) = e®²i+ 4xe®j – 5eV²k. V.(V × F) =

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Q: pind tue indefinete integral S In(s-1) ds

A: ∫ slns-1dsLet u=s-1=∫u+1lnudu=lnuu22+u-∫12u+2du=lnuu22+u-u24+uSubstitute back…

Q: Find r'(t). r(t) = (tan (6t))i+t cos(t)j – Vik I| NOTE: Enter your answer in terms of i, j, and k.…

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Q: Find V. (V x F) if F(x, y, z) = 8 sin zi + 6 cos(2.x – 3y)j + 7zk. V.(V x F) =

A: Vector

Q: Evaluate the limit 11г3 — 7? — 9х lim 10— 5х — 5а3 I+ 00

A: This question can be solved using the concept of limits.

Q: Use series to evaluate the limit. X-In(1 +x) lim

A: Find your answer below

Q: S (1/(X(Im)*) dx X(Inx)

A: LetI=∫1xlnx2dxLet u=ln(x)differentiate 1xdx=duI=∫1xlnx2dx.I=∫1u2du.I=∫u-2duUse power…

Q: Use the Taylor series for f(x) = Vx, centered at a = 16, to approximate the numerical value of v17.…

A: This question can be solved using the concept of Taylor series centered at a.

Q: ) Find an equetionof tue tenyent line to the greph of d= In(x') at the point (l,0). Angwery8 a) y*-5…

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Q: Question 8 of 10 View Policies Current Attempt in Progress Find r'(t). r(t) = (tan(9t))i+t cos(t)j…

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Q: Determine if the following function is continuous or discontinuous at x = 0? 4 +5 f(z) = 9-3z

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Q: Change the Cartesian integral to polar coordinate | +y*)dx dy

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Q: e i+ - 1 (P-1)i-(e1-1)j+글 i - k

A: Given query is to find the integral.

Q: 3/2 x*(G²- x²) %z

A: …

Q: Find r'(t). r(t) = (tan(3t))i+t cos(t)j – Vēk NOTE: Enter your answer in terms of i, j, and k. r'(t)

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Q: 1. Let -7 3 -3 2 C = 4 A = B = -3 -3 Determine which (if any) of the following matrices are well…

A: The solution is given in the nwxt step.

Q: Sy³/y² + 9dy

A: ∫ y3y2+9dyLet u=y2+9=∫u2-9u2du=∫ u4-9u2du=∫ u4du-∫ 9u2du=u55-3u3Substitute back…

Q: 6. Given f(x,y) = x² – 2xy² – 4xy + 5. Find all the critical points of f and determine the nature of…

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Q: All edges of a cube are expanding at a rate of 3 cm per second. How fast is the volume changing when…

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

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Q: 33) Find tue ared ef tue Serface formed by revolving thecirele r= f10) = 10 C6s Q f10) =10 Cos Q…

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Q: Find r'(t). r(t) = (tan-(11t))i+t cos(t)j – Vtk | NOTE: Enter your answer in terms of i, j, and k.…

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

A: Given :A≠∅A ⊆ B

Q: Evaluate the following limit using Taylor series. 7 7 tan -(x) – 7x + lim 4x° 7 7 tan "(х) - 7x +-…

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Q: For the following telescoping series, find a formula for the nth term of the sequence of partial…

A: Write the nth term and  add them to get Sn .

Q: Find y=f(x), if f''(x)=3x^2, f'(0)=-7 and f(0)=2.

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Q: Find curl (8z i + 9x j + 10y k). curl(8z i + 9x j+ 10y k) Di +(i Dj +( )k

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Q: dx 5-x?

A: We will solve the integral.

Q: Evaluate the limit 9х + 5 lim z+00 2r2 – 6x + 6

A:

Q: no1

A: Topic:- application of derivatives

Q: 2t +1 lt +8 -dt + 4t +4t 3

A: Let's find.

Q: estion 6 of 10 w Policies rent Attempt in Progress Find V (V × F) if F(x, y, z) = 8 sin xi + 3…

A: We know divergence of curl of any vector function is zero.

Q: e2 º In(2) dzr

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Q: Find r'(t). r(t) = (tan(6t))i+t cos(t)j – VEk NOTE: Enter your answer in terms of i, j, and k. r'(t)

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