1. Find the area bounded by the parabola y=4ax, the x-axis, and the lines x=4a, x=9a.

Q: Find div F and curl F if F(x, y, z) = 4y³z'i – 11a"z°j – 4xy°k. - -

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Q: plapii the function f(t) = 6t(h(t – 1) – h(t – 6)) for 0<t<o. Use your graph to write this function…

A: Heavyside function

Q: af(x, y) If f(x, y, z) = , then is equal to dz

A: Given,  f(x,y,z)=x-zy-z

Q: ydy can best be evaluated by algebraic substitution. Vy-1 A True В False B

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Q: Find the divergence of the vector field F. F(x, y) = 8xe*i – 7x²y²j |

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Q: Solve the differential equation for general solution y' = 2x - xy; y = 5 when x = 0 %3D O y =…

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Q: Evaluate the following definite integrals. år 5.

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Q: Below is a graph of f' (x), the derivative of f(x). A B D E F When is: f(x) greatest? f(x) least? f…

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Q: 3. A particular is moving with acceleration given by a(t) = 3 cos t - 2 sin t. Given that s(0) = 0…

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Q: A point Q moves along the intersection of the sphere a? + y? + 2² = 1 with the 2. At what rate is z…

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Q: Solve the problem. Solve the differential equation model of a population growth: dP 0.5P. dt O P(t)…

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Q: Use power series operations to find the Taylor series at x= 0 for the following function. 17x e* The…

A: we want to find taylor series of the function 17 x ex  about  x=0

Q: Solve the differential equation for general solution 7y6dy = 8x

A: Given query is to find the solution of the differential equation.

Q: Sketch the region enclosed by y 6x and 4x. Find the area of the region.

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Q: EXAMPLE 3 Evaluate the following integral. VI- 4.r2 SOLUTION Let u = 1 - 4x². Then du %3D , SO xdx =…

A: We can solve as follows

Q: sin a Determine the derivative of sec x sec x cos z-sin z sec tan e sec2 a O 1 1-sin x sec2 x sec2 x…

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Q: Evaluate the line integral using Green's Theorem and check the answer by evaluating it directly. 3…

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Q: Determine whether the series converges or diverges.

A: Solve the following

Q: 3. If g(x) = -dt, find g'(2). %3D

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Q: Kindly

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Q: For the series below, (a) find the series' radius and interval of convergence. For what values of x…

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Q: A company has identified that the revenue R for a particular product is given by the equation R(x)…

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Q: Let f(x) : Int dt. Find f'(x).

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Q: Find the average value of the function f) = 8-7 on the interval [0, 9]. %3D

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Q: Solve the initial value problem. x'(t) -x = 1; x(0) = 3

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Q: 4. , kr+2{cd= -3

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Q: Find V x (V × F) if F(x, y, z) = 9xyj+ 6xyz k. V x (V × F)

A: WS have to solve the vector

Q: Evaluate F. dr. F(x, y) = xi + yj C: r(t) = (9t + 4)i + tj, 0 sts1

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Q: Use substitution to find the indefinite integral. Зх + 7 (6x + 28x) 5 3x +7 (6x² + 28x) =xp.

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Q: Find the indefinite integral. (Use C for the constant of integration.) 4 dx V 81 – (x + 9)2

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Q: Evaluate the definite integral

A: Evaluate the definite integral .

Q: 1 The partial derivative of f(x, y, z) = Arctan with respect to z is xy? z³

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Q: Given: y = arctan sinh find y' at x 2 cosh 1 3(1+sinh 1) cosh 1 Oy = 1+sinh 1 cosh 1 1+sinh 1 %3D…

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Q: Find V x (V x F) if F(x, y, z) = 9xyj+ 6xyz k. V × (V × F) =

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Q: Ise Part 1 of the Fundamental Theorem of Calculus to find the derivative of the fum 8(x) = [" 1 dt t…

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Q: Which among the following is false for getting the derivative of an implicit function? O Another way…

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Q: 4. a = 20 m [W 30°S] b = 30 m [W 40°N]. Find a - b. %3D %3D

A: We need to find a-b.

Q: A piece of wire 21 m long is cut into two pieces. One piece is bent into a square and the other is…

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Q: (2n)! for 1· 3·5 ... (2n – 1).) 2"n! Use the binomial series to find the Maclaurin series for the…

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Q: Find div F and curl F if F(x, y, z) = 11y"2°i – 17x"z1ºj – 6xy°k. - div F= curl F=

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Q: Find dy/dx. x = Vt y = 9-t dy dx

A: Here, x=t3y=9-t

Q: / (3Vi-1)dt is 3 -1 by the 2nd fundamental theorem of Calculus. The derivative with respect to x of…

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Q: Find the surface area of the part of the cone x2 + y = z between the planes z = 3 and z = 8. Express…

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Q: Solve the initial value problem. 1 u'(x) = – 2; u(0) = 1 x2+1

A: Explanation of the answer is as follows

Q: evaluate y" -2y' +5y=0 y(0) =1, y'(0)=3

A: Solve the following

Q: Find the general solution of the equation. Express the solution explicitly as a function of the…

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Q: Evaluate the integral. V3/2 dr V1- r2 |

A: We know, ∫dx1-x2=sin-1(x)

Q: Solve y" – 2y = x²

A: We have to find the solution of the given differential equation.

Q: If x= tane, then cost do by trigonometric substitution. dr = (1+x2) ½ True B) False

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Q: Use Green's Theorem to evaluate the integral. Assume that the curve C'is oriented counterclockwise.…

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