FP Use the Fundamental Theorem of Calculus to evaluate: /2 13. xp x zJ55 9/u5

Q: (H.W) 1- Solve by choose M this time ( 2 x y² + 3 x² ) dx + ( 2 x² y + 4 y³ ) dy = 0 2- Find the…

A: If the differential equation Mdx +Ndy =0  is exact ∂M∂y=∂N∂x , then solution is                 ∫y…

Q: Find V · (V × F), if F(x, y, z) = 3e"*i+3.xe"j – 8ev²k. V ·(V × F)

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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: cion 3 of 10 plicies t Attempt in Progress curl (9z i + 10x j + 6y k). (9z i+ 10x j+ 6y k) = ( i )i…

A: Topic :- vector algebra

Q: fF(x)dx = -9 and Si (x)dx = . 3 tind f(x)dx Given that

A: We can solve the answer using the properties of definite integral as below.

Q: F. Change the Cartesian integral to polar coordinate 11-y !! (x² +y*)dx dy

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Q: 6. v(y) = In (y² – 8y – 1)

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Q: Show that g : B → A, g(x) = √ln x is the inverse of f. Why is f^−1(x) 6 ≠ −√ln x?

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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: 11. Let -4 А -4 -4 -3 -3 (a) (i) Show that -4 is an eigenvalue of A with corresponding eigenvector…

A: As you have asked multiple subparts so I have answered first three subparts as per the guidelines.

Q: The area of the region is. (Type an exact answer, using x as needed.)

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Q: Evaluate the definite integral. i-ej+ k 7 O el - 1 7. O el - 1 i+ (e- - 1) j+ k i- (e-- 1) j+ k O e…

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Q: 8. Find the limit: lim E1(1 130 noisieoq Isisinle bna baoes 1aq d00

A: The detailed solution is given below Thank you

Q: Find the gradient vector field Vf of f. f(x, y, z) = xSye'/z Vf(x, у, 2) %3D

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Q: 4- to --6 -5 -4 -3 -2 -1 5- ver which interval of z values is f'> 0? о (2, о) O 12, 0) 0(- 00, 2)…

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Q: Consider the following. z = x2 + y2, x = 4s + 8t, y = s +t az az and as Find by using the chain…

A: Here, the given functions are: z=x2+y2, x=4s+8t, y=s+t So, z is a function of x and y and x and y…

Q: Evaluate the definite integral. 12t dt O el2 – 1 (e-) - 1) + 2 – 1 i - (e" - 1) j +k 12 O el2 12 O…

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Q: Describe the graph of the equation. r =-18i+(1-j+:k O Itisa parabola in the plane: = -18, with…

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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.…

A: Here, the given vector function is: r(t)=(tan-1(11t))i+tcos(t)j-tk

Q: Use the graph of the function f to decide whether the value of the given quantity exists. If it…

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Q: Find [r(t) · u(t)] and [r(t) × u(t)] in two different ways. dt dt r(t) = ti + 8t2j + t³k, _u(t) =…

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

A: This is a problem related to derivative of the function. Based on the general formula and concepts…

Q: Q2 (a) Let n E N and let ở, w e R". Show that if ở · w = 0, then || ở + w||2 = || ||² + ||w||². (b)…

A: This question can be solved using the concept of dot product of two vectors.

Q: Find the second order Taylor expansion of [15] f(x,y) = (1 +4x2 +y2)1/2 about the point (1,2) and…

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Q: B. Verify if the relatin O y= xe is a səlution to yl-2y'ty =o. y = eco( 2x) is a solution to…

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Q: Evaluate the limit using L'Hospital's rule 4* – 97 lim

A: Limit

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: 71 dt Find F (x) and F (-2). 14. Consider F(x) .Co 1+t5 EGO

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Q: Find V· (F x G), if F(x, y, z) = 11xi+j+ 4yk and G(x, y, z) = xi+ yj – zk. V· (F × G)

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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: Find the Taylor series for f(x) centered at the given value of a. [Assume that f has a power series…

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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: 19) pind tue sum of tue canvergent mveryent Senies' り。 d)- 12 아 ej 60 60 80 4/6

A: 1n+4n+6=121n+4-1n+6

Q: 12) find the indefinite inteyral Inv dv 6 v3 Answery a) -L (2invtl /Ac 12 v2 bり- りよemvtiリ+c (2 12v2…

A: The given integral is ln(v)/(6v3).

Q: 3 10. S 2x Vx2 – 3x + 1

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Q: Find the limit of the following sequence or determine that the sequence diverges. 15 Select the…

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Q: Use the formula k(t) = |r(t) × r"(t)|| ||r(t)||° to find «(t). r(t) = 8 cos(7t)i+ 8 sin(7t)j + 3tk…

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Q: Find the coordinates at times t = 0, 5, 10 of a particle following the path a = 9+ 5t, y = 2 – 7t3.…

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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: 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: COSX sin x dx 4. S 1-ఆశి అరికి న

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Q: 1. Calculate the following limits (showing all working): log,(n) + 5" n-0o log7(n) + 7" Vn5 + 2 +…

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Q: 3 In ДАВС, с % 15 ст, b — 4.6 ст, тLA: = 106°. Find the area of the triangle and round to the…

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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: ||r'(t) × r"(t)|| Use the formula k(t) to find k(t). ||r(t)||³ r(t) = t’i+ t°j K(t) :

A: We have to find the value of k(t)

Q: Find the indefinite integral. (a) / (2* + v#)dx (c) / 2x6 + x5 -dx x4 (4) [(4cs (xỉ + 5x + 4)dx (4…

A: Note: As per our company guidelines we are supposed to answer the first three sub-parts of the…

Q: find the area of the region bounded by y=(x+2)^2-1, the x-axis, x=-1, and x=2.

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Q: Find the curvature and the radius of curvature at the stated poin r(t) = 11 cos(t)i + 10…

A: Here we have r→(t)=11cost i +10sint j +10t k  at=π2 The formula for curvature is…

Q: ||r(t) × r"(t)|| Use the formula k(t) to find k(t). %3D 13 r(t) = ti + t5j K(t):

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Q: Let v=f(x) be a solution of the first order linear differential equation y'=y-10x² such that f(0)…

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