Find the distance between the point and the plane. (Round your answer to three decimal places.) (1, 3, 4) x - y + 2z = 4

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A: Given; ∫01∫0xfx,ydydx=∫01∫y1fx,ydxdy   Let, I=∫01∫0xfx,ydydx The region bounded by the lines, y=0,…

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Q: sec (In x)dx

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Q: x²-9 dx Given: x3 Using trigonometric substitution, solve for the integral form in terms of 0.

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Q: Compute the directional derivative and gradient of f(x, y, z) = 4r – yez at (2, -1,0) in the…

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Q: Find the indicated derivative. f (x) = (x³ – 5x + 2)(x² + x – 7); find f"(x). %3D

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Q: 8. Let y(x) be the solution of the differential equation ry' - y = lnr such that y(1) = 1. Find y(2…

A: The standard form of the first-order linear differential equation is: dydx+Py=Q Where P & Q is…

Q: 4) Equation: 4x +9y² = 1 1 Given that dy/ dt =8, find dx / dt when (x,y)= 3 9

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Q: 1 1) [ (tan³ 0 + tan³ 0) e-tan º d0== 2 (-1)" n! (In x)" dx= (m + 1)"+1 ·

A: Note : As per our guidelines we are supposed to answer only one question if there are multiple…

Q: Estimate the area under the graph of f(x)= 3x between x 0 and x=1 using each finite approximation…

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

Q: Let R = {(x, y) ER214 < x? + y < 9}. By inverting to polar coordinates: %3D y? %3D Vx? - + y2 Select…

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Q: Use implicit differentiation to find dydx 4x^2y+9xy^2=6

A: Given that,       4x2y+9xy2=6

Q: Evaluate the integral. (Use C for the constant of integration.) (3× – 5*) dx -

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Q: Use the following theorem to evaluate the integral le - 4|dx. Theorem: Iff is integrable on a closed…

A: Given:     ∫-22ex-4dx Eliminate absolutes      =∫-22ln2-ex+4dx+∫2ln22ex-4dx…

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Q: |sin(x)cos(2x)sin(3x) dx sin(3x)cos(3x), sin(2x)cos(2x) sin(2x) 12 8 8. + C 4 sin(6x) sin(2x),…

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Q: ey+y°.

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Q: Given the area  in the first quadrant by x^2 = 8y, the line x = 4 and the x axis. What is the volume…

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Q: Find the indefinite integral. (Use C for the constant of integration.) 1 dx xV 16x2 – 1

A: Solve the  intregal

Q: Verify that the points are the vertices of a parallelogram, and find its area. А(1, 1, 3), B(—2, 3,…

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Q: Question 4 of 10 Find the volume of the solid that results when the shaded region is revolved about…

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Q: dx 1- cos 2x

A: The given integral is ∫dx1-cos2x Now,        cos2x =1-2sin2x       ⇒  1-cos2x=  2sin2x…

Q: Compute the derivative of the given function. f (x) 10x-1/4 cos e + 7 sin a %3D -

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Q: 2) Find the cartesian eauation for the olar curve r=tan e sece ×ニy )yニxと 2.

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Q: lim -1 x→0+

A: Separate the limit.

Q: %3D 15. If the vector field F(x, y, z) = xz i+ xyz j-y k, find curl F.

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Q: ニ 2 2. dx | -r

A: The given integral  y=2∫-rrr2-x2dx  Can be solved using integration formulas given below…

Q: Solve the problem. Given that f(x) = 5x², find lim [f(x) - f(4)/(x - 4)]. X-4

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Q: Use polar coordinates to evaluate the integral er+y dA R where R is the region that lies in the…

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Q: If f'(x) > 0 and f" (x) < 0, then which of the following is true? o f(x) is decreasing and concave…

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Q: 13. the , xydA, where ySxsy?}

A: First I have set the limiting double integral from given information and then solved it .Final…

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Q: 2x2 1) Given: f(x)= 48(3x +16) f"(x)=- (² –16) -8 -48x s'(x)=: (x² -16) x-16 a) Determine any…

A: Given: f(x)=2x2-8x2-16f'(x)=-48xx2-162f''(x)=483x2+16x2-163

Q: The dimensIons of awater tank are 13 cm, 10 cm and 70cm. If it is half-filled with water, cal-…

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Q: Determine the speed along a parameterized path s(t) = (9t³, 7t²) at time t = 6 (assume units of…

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Q: Consider the polar curves Cı : r = 1+ cos 0 and C2 : r = 2 cos 0, and let R be the shaded region as…

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Q: Given: dx x3 Using trigonometric substitution, solve for the integral form in terms of 0.

A: This question can be solved by taking x=3secθ

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Q: y''+4y'+3y=sin(3t) with y(0)=1 and y'(0)=-1 determine with laplace transform

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Q: 10

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Q: 9. Given arbitrary matrices A, BE RXn with n> 1, select the c of A and B). 1. tr(AB) = tr(A)tr(B) 2.…

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Q: x(z – 2y)100 = yz + x; Yx and x,.

A: Solution is given below:

Q: 3x — 1 - dx (x – 2)(x + 5) 3 In |æ – 2| + In |æ + 5| + C 3 In |æ – 2| + In|æ + 5| + C O A Ов 16…

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