A line is drawn through the point (6,4,2) perpendicular to the yz- plane. Find the coordinates of the points on this line at a distance 10 units from (0,4,0).

Q: Q4) Evaluate the following integral using Trigonometric Substitutions Method: 2 y = - x dx

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Q: Q4) Find plane area inside the polar function r = 2sin E- 0) and outside r= sin -0) in first…

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Q: -6x-'dx

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Q: æP In(x) dz a. Find the values of p for which the integral converges. The integral converges for all…

A: ∫01 xplnxdxApplying integral by parts,=1p+1xp+1lnx01-∫01xpp+1dx=1p+1xp+1lnx-xp+1p+1201=-1p+12…

Q: Is this series convergent or divergent?

A: This question can be solved using the concept of root test.

Q: At a certain instant the radius of a right circular cylinder is 6 inches and is increasing at the…

A: At a certain instant the radius of a right circular cylinder is 6 inches and is increasing at the…

Q: Find the distance between the parallel planes 10х — 5у — 52z — 26 — 0. 2х + у + 2 %3 0 and - - NOTE:…

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Q: Question Consider the function f(x) below. Over what open interval(s) is the function decreasing and…

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Q: Q2) Solve the D.E xy(x? + 1)dy - (y? + 1)dx = 0 %3D

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Q: Integral using trigonometric sub The answer in the integral is: sin(20) + C 8 4 If x= 2sece then x/2…

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Q: Find the area of the band cut from the paraboloid x² + y² – z = 0 by the planes z = 2 and z = 6.…

A: To find the area of the band cut from praboloid.

Q: Find the equations of the lines tangent and normal to the curve given by the parametric equations…

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Q: Q2) Solve the D.E dy - (2x/1– y²)dx = 0

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Q: / sin*0 d0, factor sin*0 as (sin²o)² sin® and let sin²0 = -(1– cos20). To evaluate A True False

A: Given problem:-

Q: dx = x(1 – y) dt dy у(х — 1) dt

A: Solution of the problem as follows

Q: Consider z=e (*3+y2) Evaluate dx2 O (6r2+ 3x)e (*3+y2) (9x4+6x)e (x³+y²) (6x4+ 9x) e (x³+y²)

A: Topic = Derivative

Q: Consider the following function. f"(x) = 48x Find f'(x). (Use C for the constant of the first…

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Q: Find an equation of the plane that passes through the point P(4, 5, 3) and has the vector n = (1, 8,…

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Q: 2. Use a parametrization to express the area of the given surface as a double integral and then…

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

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Q: Find the sum of the following convergent series: itan-(2n – 1) – tan-(2n + 3)]. n=0

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Q: Given: A = {1, 2, 3, 4, 5, 6}, B = {2, 4, 5, 6}, and C %3D = {1, 6, 7}. Find: (A U B) NC = O {1, 2,…

A: Given: A=1, 2, 3, 4, 5, 6, B=2, 4, 5, 6, and C=1, 6, 7.To find A∪B∩C.

Q: Q3) Evaluate triple integral y(x2-y?)dz dx dy.

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Q: To find the distance across a river, a surveyor choose points A and B, which are 232 m apart on one…

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Q: Evaluate the following integral using Partial Fractions Method: x3 + x2 y : dx x2 + x – 2

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Q: Use the First Fundamental Theorem of Calculus to answer the ff. If F(x) = tvt +1 dt, evaluate F(1),…

A: Given: Now,          F(1)=∫11tt+1dt=0. Here,               F'(x)=xx+1⇒F'(1)=2 Further,…

Q: Find the length of the polar curve r=2cos(theta) 0 < theta < pi

A: Given:         r = 2 cos θ        0 &lt;  θ &lt; π

Q: Determine whether the planes are parallel, perpendicular, or neither. Зх — 15у — 12z — 2 %3D 0 (a)…

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Q: A particle is moving with the given data. Find the position of the particle, s(t). a(t) = 4 cos(t) -…

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Q: The graph of the function fis given. y 32 24 y fx) 16 8. 8. 16 24 32 40 48 (a) Use six rectangles to…

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Q: Find the local extrema of the following function. f(x,y) = - 8x-8xy-6y + 120x + 68y + 3 Find f,(x.y)…

A: Given f(x,y)= -8x²-8xy-6y²+120x+68y+3 So, fx(x,y)= -16x-8y+120=-8(2x+y-15) And fy(x,y)= -8x-12y+68=…

Q: x² +2 dx (x – 2)(x² – 2x + 2) 1. -

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Q: PART II. Find the derivatives of the following expression, solution must be presented. 1. x²y – ỹ =…

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Q: sequence

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Q: Find f"(2) if Ax) %3D x² - 3* 08 O -7 4 O 2

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Q: Appraximate the critical numbers of the function shown in the graph. Determine whether the function…

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Q: Evaluate the following integral using Trigonometric Substitutions Method: dx y = 9x² + 16

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Q: n(A U B) = 55, n(AN B) = 15, and n(B) = 35 %3D Find the value of x A 15 y

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Q: Q5/ Use Linear Regression to fit the following data: 1 2 3 4 6 Y 4 6. 10 10 8

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Q: Find the value of x such that x satisfies the mean-value theorem at the interval [0. 1] for the…

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Q: 2. S dx I+,x

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Q: Question For the function f(x) given below, where x > 0, evaluate lim f(x). X00 f(x) = In(5x² – 5) –…

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Q: y = Vx* X

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Q: Find the distance between the skew lines: x = 4+ 9t, x = 4 – t, y = 3+ 2t, z = 7 – 4t y = 9, z = 8+…

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Q: X+ 1 Evaluate lim x→1* ** - 5x +4• | O-1 OO OO

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Q: Evaluate the following integral using Trigonometric Substitutions Method: dx y 9x2 + 16

A: We have to solve above question

Q: Consider --e +y?). 3+3² Evaluate dxdy

A: We have to find partial derivatives for the given function.

Q: (a) Find the series' radius and interval of convergence. Find the values of x for which the series…

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Q: Find the value of c where lim(x) does not exist for the graph of the function shown below a. none of…

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Q: We are told that the sand is falling onto the pile at rate of 9 cubic feet per minute. We want to…

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