Noting that C1: r=cos0+1 and C2: r=2cos0, let R be the shaded area.

Q: Rx) - х3 - х2 - 12х + 6, [0, 4)

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

Q: ds ds Draw a dependency diagram, and write a chain rule formula for др where s = g(x,y,z), x =…

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Q: A (x -3) dy X +y -.

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Q: v du is? x³ sin (x²) dx ¡s evaluated using IBP, the value of J When

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Q: Example 11 Determine the points at which the limacon defined by the polar equation r = 3+2 sin 0 has…

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Q: I 2 3 To find the blue shaded area above, we would calculate: | f(x)dx = area Where: a = b = f(x) =…

A: Here we have to find the area under the graph.

Q: Point U is on the curve y = ln(x). Let O be the line joining U to the origin. Find the coordinates…

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Q: The​ half-life of a certain tranquilizer in the bloodstream is 45 hours. How long will it take for…

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Q: Convert the polar coordinates (1, 90 ) to Cartesian coordinates. (0, 1) (0, -1) (1, 0)

A: r= 1 and theeta= 90°

Q: F- dr in the case when F(z,y) = (7y -sin (y) + 8) i+ (72 - cos (y))jis conservative, and Ais the…

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Q: If an object's position over time is given by the function d(t) = (t +3)e i for t > 0, on what…

A: We have to find range of t for which position is increasing & concave up.

Q: 1-x² dx

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Q: Given that f(z, y) = z (2y+4) +y(7z - 14) is a potential function for F = (2y+4+7y, 2z + Ta - 14).…

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Q: clear

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Q: Find f. f "'(x) = cos(x), f(0) = 8, f '(0) = 8, f(x) =

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Q: tanx sec*x dx. Use trigonometric groups.

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Q: The function f has the property that f(3)=2andf (3) = 4. Using a linear approximation to ff near x=3…

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Q: Evaluate the integral. (Use C for the constant of integration.) (2x4 – 4x-2 + 3x + 4) dx

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Q: Consider sin °x cos2x dx. f we let 4=cos x, the integrand can be transformed to

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Q: Convert the polar coordinates (1, 111) to Cartesian coordinates. O(V3/2, -1/2) O (1/2, -V3/2) O…

A: The objective of the question is determine the Cartesian co-ordinates.

Q: x²+x+1 3. Use partial fractions. 2r²+2+x³+x

A: Explained below

Q: | (In x)² dx_use integrationI

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Q: x2 V1-x2 dx Use trigonometric substitution

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Q: ah4.

A: answer is in next step

Q: Evaluate the following indefinite integral. 10 10 11x dx 10 X

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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: A rectangle is constructed with its base on the x-axis and its upper two vertices on the parabola y=…

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Q: Choose point which has the correct location for the polar coordinate(-4, 180\degree). 90° WIN A 150°…

A: see below the graph and the answer

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: f(x) Let lim = 2. Find limits below. f(x) + 6x (a) lim 2.x f(3x) (b) lim I+0 5x

A: Use the limit given above and simplify limit for a and b .

Q: A ball is being inflated such that the volume is increasing at a constant rate of 130cm3/s. How fast…

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Q: (9) If sin(A) = /2, sin(B) = - ½, "/½ < A < r, and n < B < 3*/2, find cos(A + B) (A) 0 (B) /2 (С) —…

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Q: Find two positive real numbers whose product is a maximum. The sum of the first and twice the second…

A: Given: The sum of the first and twice the second is 56

Q: 3 Find the arc length of the astroid: x = cos t, y = sinº t, 0 <t < 2T

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Q: Convert the Cartesian coordinates (3, 3) to polar coordinates. (3√2, 45°) (3√2, 60°) (3√2, 30°)

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Q: 5) The hypotenuse of a right triangle is 12 cm in length. Calculate the measures of the unknown…

A: To find the dimensions of given triangle such that it has maximum area.

Q: の Cm (1av)ー lim XDO

A: lim   ((1+x)3/2 -1)/x x  -- 0 here 0/0 for so we use la hospital rule and differentiate above and…

Q: x2+x+1 2x2+2+x3+x

A: Solution: ∫x2+x+12x2+2+x3+xdx factor the denominator ∫x2+x+1x+2x2+1dx

Q: 6x3 + 7x7 – 8x³ – 8. Consider the function f(x) An antiderivative of f(x) is F(x) = Ax" + Bx" + CxP…

A: We want to integrate the given equation.

Q: Solve this problem algebraically, using your knowledge of derivatives. Do not solve by graphing.…

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Q: Convert the polar coordinates (T, 7) to Cartesian coordinates. O ( T, TL) O(- T, 0) O (0, - T1)

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Q: ssignment : Determine the integral of the ff. functions 1. S- 6 dx 2. J5 х4 dx 3. S ( 4 x7 + 7 ) dx…

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Q: What is the numerical value of tan(0)? (Hint: what does tan(0) represent?) tan(0) Preview

A: Given that the graph where theta measure radians  To find the numerical value of tan(theta)

Q: Convert the Cartesian coordinates (-2, 2/3) to polar coordinates. (4, 150°) (4, 120°) O (6, 120°)

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Q: Evaluate the integral. 4 2х e dx 4 2x e dx = (Type an integer or decimal rounded to the nearest…

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Q: S Integrate the falloing funclinne the given kesinms aver R: y=4x-x and y =X

A: Area

Q: Find the average value of the function on the interval. Give an exact answer. f(x) =  1/(x-7)^2…

A: For average value of f, we need to integrate in the given interval.

Q: Given IV-x2+ 4x +5 dx. Using trigonometric substitution, what is the integral form in terms of 0 ? A…

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Q: S 3+4x+3 dx x4-5x2+4 5.

A: Here, x3+4x+3x4-5x2+4=x3+4x+3(x2-1)(x2-4)⇒x3+4x+3x4-5x2+4=x3+4x+3(x-1)(x+1)(x-2)(x+2)

Q: 1) Find the derivative of the following trigonometric expressions below. Please show all of you work…

A: A)y=sin x+ cos x -3x2dydx=ddx(sin x)+ddx(cos x)-ddx(3x2)dydx=cosx -sin x -6xB)y=-12…