1. Evaluate the double integral r²y dA, where D is the region enclosed by the x-axis and the semicircle y = √1 - x².

Q: Find a and b such that v = au + bw, where u = v = (7,2) a = b || || = (1, 2) and w = (1, -1).

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Q: Evaluate the following integral: dx -27 x2/3

A: Solve the following

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A: The given function,  fx=1x2+x-30

Q: For a certain automobile, M(x) = - .015x² +1.32x-7.3, 30≤x≤ 60, represents the miles per gallon…

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Q: Estimate the area under the graph of f(x) = approximating rectangles and right endpoints. R₁ = 1 x²…

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Q: If r(x) = -cos (x + 9) +7, determine the antiderivative of r(x). (Do not include the constant C'in…

A: In this question, we want to find the antiderivative of the given function r(x).

Q: Find the derivative of each function. Show all your work and simplify the result completely. a un…

A: We can answer both the question as below.

Q: Find an equation of the tangent plane to the surface at the given point. f(x, y) = X, (1, 7, 7) 10 5…

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Q: thats a natural log of 9 to 0 and integral from 9 to e^x

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Q: 1. Simplify fully. Write each expression with positive exponents only: 6a -b √√-270x (2a 5-32 √9(x)⁰…

A: Follow the procedure given below.

Q: 2 (D" +8D² +16) y = - sinx Ans: y=as2x+ C₂ Sin2x + C3 XC052 X + (4x sin2x-sinx

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Q: Find the TOTAL SOLUTION of the following Differential Equations: 1. 3 dy. dy +3 dt³ 2 dt² - 4 = 5t²…

A: Given the differential equation is d3ydt3 + 3d2ydt2 - 4 = 5t2 + 4

Q: f(x)=ax^3+bx find the derivative

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Q: Express in exact form: In(x² + 1)dx

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Q: K=1 3√√√x² +7 2 K³ +4 3 • The limit comparison test with { k=1

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Q: 1. Find the orthogonal trajectory for the family of circles with center at (-2,3) and draw the…

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Q: Find the component form of v given its magnitude and the angle it makes with the positive x-axis.…

A: To find the component form of v given its magnitude and the angle it makes with the positive…

Q: Find angle t [in EXACT form] for the following terminal points on a unit circle, 0≤ t < 2π (a) P(0,…

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Q: Find the function whose tangent line has the slope 8x² + 3 for each value of x, and whose graph…

A: To find the function:

Q: Use an appropriate area formula to find the area of the triangle with the given side lengths. a = 14…

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Q: (a) Find x, y, z and B, where Tox 37 A = 1 -3 y A² = 1; C(4+1)+3B7 = 2A, and I: unit matrix ; 4 o…

A: Please re-state the subpart (b) properly.   To find the values of x, y, z and the matrix B=?

Q: y = (2x₁³ - 6) 9 3 Find day 3 dx²

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Q: A x Given that cosa= and 0 <a<, determine the exact value of cos 3 A cos = (Simplify your answer,…

A: All trigonometry ratio are positive in first quadrant .

Q: Problem 2.7 Let Find the limit lim f(x). x 0 f(x) = x² if x is rational 0 if x is irrational.

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Q: Find the point(s) of intersection (if any) of the plane and the line. (If an answer does not exist,…

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Q: Verify that the two planes are parallel. -x + 6y + 2z = 3 1 - x + 3y + z = 4 -½-X 2 Find the normal…

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Q: Suppose that the graph below is the graph of f '(x), the derivative of f(x). Find the open intervals…

A: To find the inflection point.

Q: Without using a calculator, evaluate, if possible, the following expression. 4π 3 sin sin ...

A: We will find the value.

Q: Find the gradient of the function at the given point. Function Point (8,4) f(x, y) Vf(8, 4) = = = x…

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Q: Find the derivative of the function using Chain Rule. h(x) = (2x-6)-¹ (x²+3)

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Q: The derivative of a function of fat z is given by provided the limit exists. f(x+h)-f(x) = f'(x) =…

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Q: Find the critical points of the following function. Use the Second Derivative Test to determine (if…

A: To find the critical points of the following function. By using the Second Derivative Test to…

Q: Use the Laws of logarithms to rewrite the expression 3 (212. √/y13 in a form with no logarithm of a…

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Q: 'y-1 ++ Beson Muss 1- +

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Q: Find an equation of the plane with the given characteristics. The plane passes through the points…

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Q: A white wine at room temperature 70° F is chilled in ice (32°F). If it takes 15 minutes for the wine…

A: Given that , Room Temperature T0=32°F

Q: If cos(t): sin(t) = cos(-t) = 7 and tan (t) > 0, find sin(t) and cos(-t) 10

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Q: Without using a calculator, find the exact value of the expression: 20 cos(-315°) - 6 cot( - 135°).

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Q: e 1 Determine the equation of the tangent line y=x=2( at x

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Q: Solve the given differential equation by undetermined coefficients y" - 8y' + 16y= 12x + 6 y(x) =

A: Given:         y'' - 8y' +16y = 12x+6

Q: The height y (in feet) of a ball thrown by a child is 1 y = - -x² + 6x + 3 12 where is the…

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Q: Find the inverse function and graph both f(x) and f(x) on the same set of axes. Check your work by…

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Q: Tutorial Exercise You are given the dollar value of a product in 2016 and the rate at which the…

A: topic- linear equations

Q: 10. (a) Construct the Taylor polynomial p3(x) of degree 3 for the function f(x) = 1/(2-x) around x =…

A: Solution is given below:

Q: 4 n=n? + 2n 1 4. Σ -(x-3)"

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Q: 1. Set up the formulation to find the surface generated when the curve y = x² is revolved about the…

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Q: Find the area of the region bounded by the graph of ​f(x)=sin x and the​ x-axis on the…

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Q: Use Theorem 13.9 to find the directional derivative of the function at P in the direction of the…

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Q: нх У - 169 = 19.2 ё + воё, усо) =ўс) 4Х 4X -4Х Ans: y=2.2 +e+24xe X - Че

A: Solution of given question is written in below steps.

Q: The number of traffic accidents per year in a city of population p is predicted to be T 0.002p ³/2.…

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