Find the general equation of the plane containing the point (2, –1,4) and normal to the line 2 = = I+3 y-3 %3D = Z. 3

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A: Since you have asked multiple question, we will solve the first question for you as per our guide…

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A: As per our guidelines we are supposed to answer only one question. Kindly repost others question as…

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Q: x²+2x-63 1. a) Find the value of lim, x-7 10*-10-* b) Evaluate lim,¬ 10*+10-x

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Q: () Write the linear system in matrix form. Assume X = dx 3D —Зх + 5у — 92 dt dy 3 4x — у dt dz = 10x…

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A: On solving this we will get:-

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Q: 8. Evaluate the integral by using trigonometric substitution 2 dx V4x – x2

A: We have to find the indefinite integral.

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A: answer is in next step

Q: [x² sin 3xdx

A: By Parts Method: ∫u(x)v(x)dx=u(x)∫v(x)dx-∫dudx∫v(x)dx ∫sin3xdx=-cos3x3∫cos3xdx=sin3x3

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Q: 8x, + 4x - X3 = 11 -2x, + 5x, + x3 = 4 2r, - x2 + 6x, = 7 4 %3D

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Q: Find a solution to the SDE dX = X,(ydX;+ tdt), where y E R is a constant and Xo = 1. %3D

A: This is a problem of differential equation. Based on the variable separation method we will solve…

Q: Find the gradient of the function at the given point. f(x, y) = 5x + 3y2 + 5, (1, 5) Vf(1, 5) =

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Q: 2. Sketch and identify the graph of the equation a+y? - 2y-3 0 in 3D.

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Q: 2 sin? x lim х-0 5x(1+сos x)

A: Let L=limx→ 02sin2x5x1+cosxlimx→ac·fx=c·limx→afxL=25limx→ 0sin2xx1+cosxPlug in the value…