Represent the plane curve by a vector-valued function. x2 + y2 = 36 r(t)

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

A: Given,  f(x,y,z)=x-zy-z

Q: Evaluate the line integral | -ydx + xdy along the curve C : y? = 18x from (18, 18) to (0,0). NOTE:…

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Q: Find V. (F x G), if F(x, y, z) = 3xi +j+ 10yk and G(x, y, z) = xi + yj – zk. - V. (F x G) =

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Q: Q2/ Check the symmetry of r² = -sin(20) %3D Ans./ Symmetry about the origin

A: Symmetry

Q: Determine whether the improper integral converges or diverges. Evaluate the integral if it converges…

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Q: Find the derivative, dy/dx: y = log3 (2x +1) Oy =- (2z+1)3 In 3 Oy = (2r+1) In 3- Oy= log, e (2z+1)3…

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Q: 1. If y = 3x + 2x3 - 3x + 2 find Set A. d'y/dx?

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Q: Find the indefinite integral. (Use C for the constant of integration.) 5 tan(7x) sec2(7x) dx

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Q: x* +x? 5. lim, +* e* +1 In x 6. lim, csc(6x) csc(2x) 7. lim 5x+ 2lnx 8. lim, X+3lnx 2Tan 'x-x 9.…

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Q: 2. (Section 9.2) A refinery produces both gasoline and fuel oil, and sells the gasoline for $4.00…

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Q: The distance traveled in the time interval 0 <t < 4 is given by the following. -4 r4 |t2 + 6t – 16|…

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Q: dx Solve the separable differential equation dt and find the particular solution satisfying the…

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Q: S- 3 dy 3y - sin –+C 4– 9y2 3 A True B) False ||

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Q: Let f (x, y, z) = xyz. Determine the value of fryy + fyay – 2 fyyr Simplify your answers.

A: We have to find the value.

Q: Find the integral. 4 9) x4 In 2x dx A) 391.74 B) -202

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Q: 4. Perform the indicated multiplication of the two differential operators: (D –x)(x²D– 2x).

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Q: e2x 2.) S. dx ex – 5

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Q: 3 19. S Vy tan" Jy dy Ans. 2/3 n-"-2+ln 2 |

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Q: Determine the derivative of the given function: ソ=c 3 y = e x2

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Q: Suppose a product's revenue function is given by R(g) is units sold. 5g? + 500g, where R(g) is in…

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Q: Question 4 Given the following equation, determine y'using the methods discussed in class a - y3 =…

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Q: 3. [sinh ot e"dt Ans.

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Q: Find the general solution of y'' - 2y' - 8y = 24(x2+1)e4x by using VARIATION OF PARAMETERS

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Q: Refer to the given below. Find the indefinite integral. Simplify your final answers (Just like how…

A: i)∫(2x3+12x2-5)dx=∫2x3dx+∫12x2dx-∫5dx                                   =2∫x3dx+12∫x2dx-5∫dx…

Q: q(x) = 0.01 (x – 136.7)2 – 106.17 r(x) = 9.5 sin(0.3(x – 245.7))+11.8 s(x) = -2 cos (-1.9(x –…

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Q: Let f(x) = x - x? on 0, 1]. f(0) f(1) = Find c such that f'(c) = 0 or, if Rolle's Theorem does not…

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Q: Describe the graph of the equation. r = (5 – 31) i – 1ltj O Itis a line in 2-space that goes through…

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Q: A net is dipped in a river. Determine the flow rate of water across the net if the velocity vector…

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Q: Find the area of the quadrilateral lot shown in the figure below to the nearest square foot. 130 ft…

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Q: sin(ry), Which of the following is TRUE for lim(z,1)>(0,0) Lütfen birini seçin: a.The limit value is…

A: Limit

Q: dy Given the equation below, find dæ - 51a" + 7a"y + y10 = - 43 dy 172 (15 – 1422y) 29. dæ Now, find…

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Q: The circumference of a sphere was measured to be 76 cm with a possible error of 0.5 cm. Use inear…

A: Given problems:- 1).    The circumference of a sphere was measured to be 76 cm with a possible error…

Q: Evaluate the line integral -ydx + xdy along the curve C : y? = 30x from (30, 30) to (0,0). NOTE:…

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Q: bounded by the graph of the function and the x-axis over the given interval. (Round your answer to…

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Q: find the volume of an ellipsoid having the equation x^2/25 + y^2/16 + z^2/4 = 1

A: Let's find.

Q: Determine f„ (0, T, 1), fy(0, , 1), f¿(0, r, 1) given the function z sin(3xz+ y²)

A: The given function,        zsin3xz+y2

Q: 3e dt 10. SET A.

A: We will use the concepts of definite integral

Q: Find the divergence of the vector field F. F(x, y) = 4xe*i – 3x?y?j

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Q: ermine the Interval(s) for which the function is (a) increasing, (b) decreasing, and (c) constant.…

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Q: 5 x X LOS

A: Given: I=∫0πsin5x2cos7x2dx  ...1   As we know that; The Power rule: ∫xndx=xn+1n+1+C

Q: arcsin = ab' a? - Va? - y?; Find y!. Oy = 2abr(x+b) Va-y 1-y 2ab r Va- 1-y 2ab r/a-y H. 1-2ab z a- «…

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

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Q: ||r'(t) × r"(t)|| Use the formula k(t) to find k(t). r(t) = e"i+ e¬'j K(t)

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Q: Describe the graph of the equation. r - 12cosri + 5sinsj -k O tis an ellipse in the z = -1 plane,…

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Q: |i cos t?dt can best be evaluated by: A Trigonometric Transformation B) None C Integration by Parts…

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Q: dx 3-x

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Q: Find y': y = arc sec(x²) y = xVx - 1 2 y : xVI -x 2 y = xVx -1 x Vx - 1

A: Given: y=arcsec(x2)y'=dydx=ddx(arcsec(x2))We know that ddx(arcsec(u(x)))=11-1(u(x))2…

Q: Find the Maclaurin series for f(r) using the definition of a Maclaurin series. [Assume that has a…

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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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