3-4x-10 x²-x-6 dx.

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Q: Find the divergence of the vector field F. F(x, y, 2) = In(7x2+ 6y? )i + 42xyj + In(6y2. + 72² )«…

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Q: Find the general solution of the given linear diff eq. y'' - y = cos(x) - 5sin(2x) by VARIATION OF…

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Q: 2r-4-x 2-2r 3 in Ir+1+3Inlx-3|+C +1-3hx-31 +C Option 1 Option 2 2 In Ix + 1-31nlx-31+ C 2 In Ix+ 1+3…

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Q: Find V (V x F), if F(r, y, z) = 7e""i + 2xe"j- 3e""k.

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Q: d Calculate r1(t) · r2(t)] and dt d [ri(t) × r2(t)] first by differentiating the product directly…

A: Given that,       r1(t)=9t i+4t2j+5t3k,   r2(t)=t4k

Q: Calculus Question

A:

Q: EVALUATE EACH OF THE FOLLOWING INDEFINITE INTEGRALS. Show step by step solution. 1. dx dx 2. xV4-x?

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Q: [In(y+2)dy Ans. 3 ln 3- 2 15. -1

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Q: 1. Solve the differential equation: xy' – y = 2x In x

A: Use linear differential equation concept

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

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Q: Let s(t) (2)a v(t) = Where does the velocity equal zero? [Hint: factor out the GCF] 4+12t2 36t be…

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Q: Suppose a product's revenue function is given by R(g): is units sold. Also, it's cost function is…

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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: 4x2-3z-2 Given a+1 determine y"

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

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Q: Find the second derivative (y") of the given function: 6. y 2-e -6e* +12e-e" (2-e*)" 6e* (2+e*)…

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Q: 13. Compute the Laplace Transform of f(t) = t°e" +e* sin3t. 4 1 A) (s+ 2)'s² +4s + 13 2 B) (s –…

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Q: (a) / Which of the following integrals is equal to -2+ In 2? X - 4 dx (a) 4- I dx (b) 2 - 4 da (c),…

A: To find which of the given integrals has given value

Q: Find r'(t) r(t) = 6Vti + t²V¢j + In(2 )k r'(t) =

A: Given r(t)=6ti+t2tj+ln(t2)kThat is…

Q: No new data to save

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Q: 5. Differentiate with respect to x: SET A. 5e

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Q: Find div F and curl F if F(x, y, z) = 13y z'i – 13x°2°j - 4xy°k. div F= %3D curl F-

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Q: Write the given (total) area as an integral. a. The area above the x - axis and below y = 4 – x? b.…

A: area under the curve

Q: Find the volume of the solid that results when the region bounded by x=y^2 and x=4y+5 is revolved…

A: Given: To obtain the volume of the solid when the region bounded by x=y2 and x=4y+5 is revolved…

Q: įy'ny dy 2e' +1 Ans. 9. 13.

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Q: find Fourier series on [0,2n] 0 0<x<7 (7) f(x) =. 1 T<x<2z

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Q: Find the derivative of the function: y = (e**)e Oy = e (e*+ + 1) Oy - (e") (e*+* +1) Oy = (e…

A: We know that derivatives of  d(xn)/dx = nxn-1. And d(ex)/dx = ex.   Here i attached the solution of…

Q: 1

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Q: 3. Compute f(x)dx 2х if x<1 f(x) = { 4 if x21

A: As we know from the property of the definite integral. ∫abfxdx=∫acfxdx+∫cbfxdx And The Power rule:…

Q: 7. 1 (x dy – y dx) = 0 %3D x² + y²

A: Here, the given DE is: 1x2+y2(x dy -y dx)=0...(1)

Q: Find the following for the given equation. r(t) = (e-t, 4t2, 9 tan(t)) (a) r'(t) (b) r"(t) = %3D (c)…

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Q: Suppose the revenue function for a product is given by the function: : R(g) = - 8g° + 4g where q is…

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Q: Write a real word promble to compare fractions the solve the problem

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Q: (ye» dy Ans. (3e* +1) 4 11. 0

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Q: Find the second derivative of the function x2y – 2 = 5x + y

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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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Q: Find y': y arcsin Oy =-- %3D Oy = - zV-9 %3D Oy = %3D zV-9 %3D -69

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Q: Use the Fundamental Theorem of Calculus to find the "area under the curve" of f(x) = 8x + 7 %3D…

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Q: 2 and common ratio Write down the first four terms of the geometric sequence with first term (Type…

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Q: 2r-4x2-x-3 dx x- 2r 3 In Ix+ 1 +3 ln|x-3| + C +1-3 ln|x-31+ C Option 1 Option 2 2 In |x + 1| - 3…

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Q: Consider f(x) = (5x + 11)2022, find: i. f'(x) ii. f"(x) iii. f''(x) iv. fiv (x) v. f°(x)

A: Given, f(x)=5x+112022

Q: 2 x – 4 dx .2 1

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Q: SHOW THAT THE DIFFERENTIAL EQUATION IS LINEAR EQUATION OF ORDER ONE 1. (3xy + 3y – 4)dx + (x + 1)…

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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: A balloon is rising vertically over a point A on the ground at the rate of 15 feet per second. A…

A: Let's draw the diagram first Given: dhdt = 15 ft/sec We have to find the value of dydt when h=40

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

A: We know, ∫dx1-x2=sin-1(x)

Q: In sketching the graph of y=f(x) = – 3cos +)+4, we translate the graph of y = - 3cos s 5 by 4 units…

A: Transformation of graph

Q: Question 6 Determine the derivative, y': y = log, (In a?) %3D Oy = z In 5 In a Oy = = z In 5 In z Oy…

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Q: Find all the critical points of the function f(x, y) = x³ + y³ – 9x2 – 21x – y - 66 and label them…

A: Local Extremum values:              Consider the function f(x,y) .For critical points , fx(x,y)=0…