Find an equation of the plane with the given characteristics. The plane passes through the point (18, -16, 9) and contains the line given by  x/2 = y − 4/−1= z

Q: Q: Find the inverse (by any method you want) of the following matrix 31 1 4 3 1 3 4]

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Q: DO NOT include spaces in between characters. * Using implicit differentiation, find the slope of the…

A: We can solve this as follows:

Q: Find the derivative of f(x) = -2x Or) - 6x2 Of (x) = -6 x2 Of (x) = -6 x3 %D Or-6x* f (x) = 6 x4 %3D

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Q: Choose the suitable function y1, for the method of reduction of order, to find a second solution y2…

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Q: R={ (x,y): 0<x, 0<y, x²+y? <9} be enclosed region. The result of the following double integral (by…

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Q: wo linearly independent solutions of the differential equation y"-4 y=0 are O y,=e** and y, = e 4x…

A: I am attaching image so that you understand each and every step.

Q: Question 13 2 ydy if we let y=z+ 4, then the new integral becomes - у-2 dz In z+ 4 - 2 T True (F)…

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Q: Qel Find the limis hth G8h alie んう0 2lim 土 2x2_8

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Q: Q3) Find the Area bounded by the curves y? = x and x = 2y – y?.

A: The given curves are; y2=x &amp; x=2y-y2   Now find the point of intersection between the curve y2=x…

Q: €x2 + 5х + C) dx %3D Зх + 5

A: Given: ∫32x2+5x+Cdx=3x+5

Q: x2 In solving for the antiderivative of f(x) = Fusing trigonometric substitution, Jf(x)dx is V4- x²…

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Q: Question 6 xdx can be solved by either algebraic subsitution or integrataion by parts. х - 1 T True…

A: We solve it by integration by parts.

Q: Draw the graph of the following relations and/or functions. Make sure that all "important" points…

A: As per our guidelines, we can answer only one question in a single request. Kindly re-post the other…

Q: Use the Trapezoidal rule with step size Ar = 1 to appoximate the integral f(x)dx where a table of…

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Q: 4.) f (x) = %3D x3 5.) f (x) = 2x² + Vx

A: we have to find the differentiation of given function

Q: Determine the slope of the tangent to the curve y – 3.xy +2x =4 at the point (3, 2).

A: curve :  y2-3xy+2x2=4differentiating w.r.t…

Q: dz ins- , if we let y=Vz+4, then the new integral becomes z+4 -2 у-2 True B False

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Q: olve the following Initial Value Problem: y" + y-6y 0, y(0) = 2 y (0) = -1. and %3D %3D %3D

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Q: Find y' if 4 cos x cos y = 3y. %3D

A: To find the derivative.

Q: In S-2 dz 2ydy if we let y=z+4, then the new integral becomes Vz+4 -2 y-2 A True B) False

A: Given ∫dzz+4-2

Q: In x²/25+ x² dx , we let x=5sine. A True

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Q: R={ (x,y): 0<x, 0<y, x² +y? <9} be enclosed region. The result of the following double integral (by…

A: We have to find value of given double integral.

Q: Consider the functions f(x) = -2r + 15 g(x) = x² h(r) 16 A graph of the three functions is provided…

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Q: 1.) f (x) = 10x10 4.) f (x) = %3D 2.) f(x) = x² – 9 5.) f(x) = 2x² + Vx 3.) f (x) = –x5 – x-3 – - x

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Q: to this answer. Evaluate the left-hand limit of as f (x) = x8. 16-2x O 1/2 O -1/2 O undefined

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Q: 2 3) -2

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Q: sin x Let g(x) = 1 ot. Find the derivative d'(x). '2 1+t3 none of the choices cos X 1+ sin3x sin? x…

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Q: Write Tif the statement is true, or F if it is false. Write your answers on the blanks. dx x +C 3 2.…

A: 1.∫5x233dx=∫53x23dx=53x5353+c=x53+c1. T2.∫-45x544dx=-45x944×49+c=-5x94+c2. T

Q: Su Find D. andR X -1 %3D Xマ→!

A: Explanation of the answer is as follows

Q: Question 3 хаx S- can be solved by either algebraic subsitution or integrataion by parts. x- 1 T…

A: The given integration,         ∫x dxx-1

Q: ,R(x) dollars is the total revenue from the sale of x television sets: R(x) = 600x 20 i) Find the…

A: Rx dollars is the total revenue from the sale of x television sets: Rx=600x-120x3i To find the…

Q: (2х+3) dx (x2+3х-6)9

A: ∫2x+3(x2+3x-6)9dx=∫(x2+3x-6)-9 (2x+3) dxusing formula∫fn(x) f'(x)dx =fn+1(x)n+1+chere, f(x)=x2+3x-6…

Q: 3 dx (3) x? +9 -3

A: Topic = Integration As per guidelines , At a time only one question can be answered. please repost…

Q: Consider the region bounded by the curve v= x2 – 1 and the x - axis over the interval [0,3]. Find…

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Q: Q14. The value of lim et3 -x tan x-cos x x2 is? -

A: use l hospital rule for solving for the integral.

Q: (3-y Q1) Evaluate the integral dx dy using polar coordinate

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Q: Question 2 Evaluate: J y* sech (e m)tanh (e ) dy A sech (y7) + C B) None © -eh*(,) + C E

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Q: The antiderivative of [Vx²-25 dx is x2 – 25 – sec-lx+ C. A True B) False

A: ∫x2-25xdx

Q: S- dy - = 2/y- 5in|Vy+ 5| +C Vy +5 А) True B) False

A: ∫dyy+5Let y+5 =xdifferentiating on both sides12ydy=dx=∫2y dxx=2∫x-5xdx=2∫(1-5x) dx

Q: Let R be the region bounded by y =x+4, y=0, and x=4. Draw the region R, and evaluate the following…

A: I am attaching image so that you understand each and every step.

Q: Q1) Evaluate the following integral using Partial Fractions Method: y = : x³ +x? dx х2 +x — 2

A: Given: y=∫x3+x2x2+x-2dx   We know that; The Power rule: ∫xndx=xn+1n+1+C And ∫1ax+bdx=1alnax+b+C

Q: If u,v,w are three vectors such that each is inclined at an angle of 4 with the other two, and that…

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Q: dy Find if yJx-9 =Xyt2 %3D

A: we have to find dy/dx

Q: (a) Given a vector A =-i+ 2j – 2z in Cartesian coordinates, (i) sketch vector A, (ii) find its…

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Q: "u,V.w are three vectors such that each is incined at an angle of 4 with the other two, and that lul…

A: To find the scalar product of two vectors with the given conditions.

Q: dr Evaluate: EV9 + 4 A f (x) = = - 9r² + 4+2 +C 3x B f (x) = -4 ln 9x² + 4+ 2 +C 3x ©f(r) = -2 In…

A: A detailed solution is given below

Q: dy Vỹ+5 - =2/y- 5ln|/y+ 5| +c A True B) False

A: follow next step

Q: 6.Find all the first partial derivatives of each function x² – y² c. f(x,y) ху с. = d. f(x,y)=e* cos…

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Q: TVy+1-2 dy can be evaluated conveniently if we let x=VVy+1-2 and dy = 4x(x² +2)dx. T True F False

A: follow next step

Q: dy Find given x'+y' =8xy. dx Note: Enclose all terms in a parenthesis if either the numerator or…

A: Here, the given equation is: x3+y3=8xy...(1)