valuate √ F. dĩ where F =< y²³z, xy², az >, and C' is given by F(t) =< tª,t,2>, 0≤ t ≤

Q: Function P(X,y) a In (X*nyt),+tan"() Check the dif ferential equation.

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Q: Find the antiderivative of  x4(5x5 + 1)5

A: To find out the antiderivative we use u- substitution method

Q: Q1. f(ath) - fla) = - 1hac? +2hu-3hza+Ih2+5 h3 %3D Find f'(x)

A: To find f'(X)

Q: 1. Which of the following functions have a derivative of zero? a) y = 9.8 b) y= 11 c) y=-4+x d) y =…

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Q: Choose the correct answer     If A = {x: 0 <x <2} and B = {y: O <y <1/2) Find C = AU B and D = A…

A: Provided information is ; A = {x: 0 &lt;x &lt;2} and B = {y: 0 &lt;y &lt;1/2) we know that ; AUB =…

Q: 2. Show that the function u p(ry) + Vry v(y/x) provides the equation Pu = 0. ду? dx²

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Q: If y = xsin then y is equal to = X" at x =

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Q: dy Find for the given implicit functions: dx а) у? - ху%3D2 b) 2.x sin (xy)– x = 0 c) (xe')" + y = 3

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Q: defermine the appvoximate volume of cyliuder height 1,002 cm and diametev of 2,002 cm , using…

A: Given: height (h) = 1002 cm  Diameter (2r) = 2002            r = 2002/2 = 1001 cm  Now ,find the…

Q: B) If f(x.y) x'y? +x*y , find: axdy *Əyər

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Q: Assume that f(x) and g(x) are both differentiable functions. Given f(3) = -2, %3D g(3) = -4, f'(3) =…

A: f(x) and g(x) are both differentiable functionf(3)=-2, g(3)=-4, f'(3)=8 and g'(3)=2h(x)=3f(x)g(x)+2

Q: Find all values of x for which the tangent line of f(x) = A B С D -9 0,-9 -9,9 0,9 x²+18x+96 is…

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Q: f lx.y) = x³ - byt +ll Investigate the local + 3xy" - 6x² extremum paints ofthe function determine…

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Q: Find extrenhum of one of the following function 1. 2(a, y) = sin2(x- 0.5) + artg (y- 0.5) rE (-1,1],…

A: Let us find the Extremum of the given function in the next steps.

Q: dz 6. If z²x²y (where x, y, and z are positive), then what is dt dy dt e C given that dz dt BU Font…

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Q: find √x² ds along the line of intersection of the two planes X-Y+z = 0 and x+y+ 2z =0, From origin…

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Q: For the function f(x,y) = 6 of find and 8x+3y' dx dy

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Q: 12. Find frxyz for f (x, y, z) = sin (3x + yz)

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Q: f ▼ is defined by V= d/dx i + d/dy j + d/dz k and A& functions then show that V.(A+B)= V…

A: ∇=ddxi+ddyj+ddzkA and B are differentiable function then ∇.A+B=∇.A+∇.B

Q: 4. y2 +2xy 4, find y" Ans. y" = (x+y)

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Q: dx =7 %3D -3x イ+2e

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Q: The vertices of the triangle element fit on the coordinates (x1 = 1, y1 = 1), (x2 = 6, y2 = 1) and…

A: The vertices of the triangle element fit on the coordinates (x1= 1, y1 = 1), (x2 = 6, y2 = 1) and…