23. Consider the circle x² + y² = R². (a) Write down parametric equations to traverse the circle once. (b) Show that the length of the circumference is 2πR.

Q: If a sphere passes through the points A(0, 1, 2) and B(−1, 2, 2) and its center C lies on the…

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Q: For the following exercises, find aj dt and direct substitution. 226. f(x, y) = x¹, x=t, y=t using…

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Q: -5x² +11x+2 x(x+1)² dx 2ln|x| +3 In|x +1| + + + C x+1 Option 1 2ln|x| +3 In|x +1| +++ C Option 3…

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Q: Find the acute angle between two tangent lines at point of intersection between two curves xy = 5…

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Q: Find the area of the region bounded by y² = 4ax and x² = 4ay.

A: We have to find the area of the region bounded by y2=4ax and x2=4ay.

Q: Compute[x² sin(2x)dx. A.- x² cos(2x)+ xsin(2x)+ cos(2x)+C 1 1 B. — — x² cos(2x)+ —…

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Q: 2r find the moment with respect to the wavic of the area hounded by the parabola v - Av-172 and v

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Q: 0 W³ 6w² +3 dw

A: Given, ∫01w36w4+3dw

Q: 11. Evaluate 1 (a) √x (x² +1)³dx, (b) fdx (c) fda (d) fx x+2 ev dx √x²+4x IT'

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Q: Find the area bounded by the parabolas (x-3)² - 16ky = 0 and y² - 16k (x-3) = 0.

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Q: f/² sin() cos() sin() dx (Consider initially the first 2 terms)

A: We have to find the integral.

Q: 2π 3 [³* sin(y) + sec² (y) dy

A: We have to evaluate the given integral.

Q: Find the area bounded by the parabolas (x-2)²-9py = 0 and y² = 9p(x-2).

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Q: Find the volume generated by revolving the area bounded by x² + 4x + 4y + 8 = 0 and y=-2 about the…

A: We have to find the volume.

Q: Solve for the Partial Derivatives and total differential of each of the following function

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Q: Evaluate the y' and Simplify the answers Inverse trigo functions y = √x² - 4+2arc(csc)

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Q: Use the limit definition of the derivative to find the instantaneous rate of change o ƒ(x) = 5x² +…

A: We have to find rate of change

Q: Ji 16 sin² x cos² x dx dx B

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Q: Evaluate the following integrals. 13 1 sin²x -dx

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Q: Evaluate the integral (Trigonometric Substitution) 1 (b²y6 – y³)źdy

A: SOLUTION-

Q: The most convenient way to evaluate A) True B False 2x-3 S- -dx is use Integration by Parts. x²-3x+5

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Q: 6. Determine the Cartesian (scalar) equation of the plane that... a) contains the points (6,1,0) and…

A: SOLUTION-

Q: 5. Determine vector and parametric equations of the plane that... a) has the scalar equation 2x-y+…

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Q: 2. z = ²+² У Х

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Q: a. For the following function, find f'(a). b. Determine an equation of the line tangent to the graph…

A: This question can be solved using the concepts of application of derivatives.

Q: . Compute for the relation between the cubic inch and the cubic cm by taking the ratio of the volume

A: 1 inch = 2.54 cm    1 cubic inch  = (1 inch × 1 inch × 1 inch)  = (2.54 cm × 2.54 cm × 2.54 cm)  =…

Q: (b) p = 2 sin p cos 0

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Q: example of properties of definite integral

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Q: dx x√x-1 dx √8+6x-9x² 3. S 4. S

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Q: Find a set of parametric equations for the curve of intersection of the paraboloid x² + 4y² -z = 0…

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Q: 7. xdy = (5y + x + 1)dx Ans: y = -x-+cx5

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Q: Ja cos³ 0 sin 20 de

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Q: Evaluation. 1. Determine the antiderivative for each. Show complete solution. √ 5x³=3 dx 2. √(√x√x +…

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Q: x2 (x+2)³ dx In Ix + 2) + 4x+6 (x+2)² +C In Ix + 21 4x+6 (x+2) +C

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Q: The trough in the figure is to be made to the dimensions shown. Only the angle can be varied. What…

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Q: Let C be the parametric curve defined by Ja(t)=1²-t-6, [y(t) = 41³ + 3t² - 6t. Determine the point/s…

A: a) Given that: xt=t2-t-6yt=4t3+3t2-6t For a horizontal tangent line, the slope must be 0. That…

Q: Determine the center-radius Form of the equation of the sphere whose diameter has endpoints at (2,…

A: The first question has been solved as per the request of the student.     The center radius form of…

Q: the particular solution

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Q: -0.45|-2.8x - 4.06| 2.5

A: Here we have -0.45-2.8x-4.06-2.5

Q: Compute*cos(Inx)dx. 1 A.-—-e (cos1-sin1) - 2 2 1 B.- e 1 C.-e TT 1 2 e

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Q: Find the area bounded by the parabolas (x-3)² - 16ky = 0 and y² - 16k (x-3) = 0.

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Q: N|- x² Given: quadric surface S with equation (y - 3)2 - 2 (a) Determine and identify the traces of…

A: Quadratic surface S with equation y-32-x22-z22=1

Q: A payment of $2,690 was due two years ago, and a payment of $1,650 is due today. What single payment…

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Q: (ii) tank (In x) = x²-1 x² +1

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Q: For what value of the constant c is the function f continuous on (-∞, +∞)? cz +4 if x ≤ 10 f(x) =…

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Q: A certain family in Sitio Calculus opened a t-shirt business last year. The family started with 50…

A: Given: fx=x2-2x+3 Since, the marginal cost function is the derivative of the total cost function,…

Q: 2.which of the ff.is the reverse process of chain rule?a additional rule b.product rule…

A: Reverse Process of Chain Rule:       The chain rule for derivatives allows to calculate the…

Q: Determine the value of x when the slope is its maximum for the function f(x)=2cos(3x)

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Q: The curve defined by R(g) = 1. Considering f(g) to be a function such that f (1) = 0 and f' (1) =3.…

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Q: Find the derivative of f (y) = 153/g In(y)

A: Given: f(y)=15y3lny