Test for exactness of the DE using ∂M/∂y and ∂N/∂x 2xy − 9x2 + (2y + x2 + 1)y′ = 0. Show complete solution.

Q: (xy+ yz+ xz)dV B = {(x, Y, 2) | 0 < I < 5,0 < y < 4,0 < z< 7} . Do not round. Hint: dV can be…

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Q: dz at the point (3,2, 1), where z is defined implicitly by the equation z +z²x² – y = 8 Calculate dx…

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Q: Determine the direction at t= pie/2 where R is 2sin t i + 2 cos t j + 2t k

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Q: ವಿ 1+

A: We find value of given  integral

Q: osen y

A: Is it sen y =x

Q: Calculate using polar coordinates: 1-x² x. y. √ x²+y² dy dx So So

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Q: 5. Find if y = sin(vT +1). dr %3D

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Q: Evaluate . y? cos(x) dx + 2ysin(x)dy where C is the straight line between (0,0) and

A: The equations of the straight line joining (0,0)to π2,1 are x-0π/2-0=y-01-0=t(say) i.e. xπ/2=y1=t…

Q: Verify that the function u, defined by u(t, x) = t sin(x – t²), is a solution to the equation ,2 U +…

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Q: Q2: Find ôf ôf - for the function f(x, y, z) = x²y+ y° + xz² and Əx 'dy

A: We will find out the required values.

Q: Given y2 - 2xy = 1 a) Find y' b) Find y" and make sure your answer y" is in terms of x and y only.

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Q: Find y'(0) and y"(0) from the following table ofvalues: X 0 1 2 y 4 8 15 3 4 7 6 5 2

A: From the given table upper digits are values of X and lower digits are values of Y(X).

Q: 1. a- Find a result by using variable separation for ý=secy h- xy = x + y

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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: af af and for dy 5. Find f(1, 9) = 1+2² + y²"

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Q: STU વપ (y-1) Ty

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Q: Calculate the rectangular approximations R1, R2, and R4 for f(x)=2x−1 over the interval [1,5].

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Q: c) Show that y(x) = 1+ax+bx², where a and b are non-zero, is a solution to Laguerre's equation, d²y…

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Q: 3. Let f(x, y) = x sin xy. Find: (a) fæ(x,y) (b) fy(x,y) (c) fyy(x, y) (d) fyæ(x,y)

A: From the given function: fx,y=xsinxy As we know that: The chain rule: fgx'=f'gx·g'x The product…

Q: 3. Use cylindrical coordinates to evaluate 3 √9-x² [² [³²*² [√²²+³ (2² + y²) ³¹ dzdydz 0 Jo

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Q: express the parametric curve in the form y = f (x) c(t) = (4t − 3, 10 − t)

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Q: ScF· dĩ, where F(x,y) = (6x - 2y)7+x²7, and C is the line segment Evaluate from (6, -3) to (0, 0).

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