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Q: Jx cos 3x dx Using Integration by parts, what should be the u and the dv? O u = xdx, dy = cos 3x Ou=…

A: Given : ∫xcos3xdx    To Find : Value of u and v in integration by-parts

Q: Q4: Solve the following exact differential equation: 2xydx + (1 + x2)dy = 0

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Q: Find the critical point of the function f(x, y) —7- 5х — бх?+ 5у — 4у? This critical point is a:…

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Q: 4. For the following motion equations = 2t° - 15t + 36t – 22, t>0 a. Find the velocity and…

A: A detailed solution is given below.

Q: Given the function f defined as: f: R-(2} R X+4 f(x) = %3D 2x-4

A: Here, the given function is: f:ℝ-{2}→ℝ and f(x)=x+42x-4

Q: To find two real numbers whose sum is 23 and whose product is maximum, we should find the maximum…

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Q: %3D Find the derivative of y = Vsinx COS I 2sin z 1. -sin z H S00 5.

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Q: Suppose a Cobb-Douglas Production function is given by the following: P(L, K) = 50L0ºK®1 where L is…

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Q: Circle

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Q: Obtain the general solution to the equation dr +r tan 0 de sec 0.

A: Given first order differential equation is drdθ+rtanθ = secθ. We have to find general solution of…

Q: Evaluate the integral: So V1+ 8xdx 3 *Input answer as a decimal. Round-off to 2 decimal places.

A: Given query is to find the value of the integral.

Q: Show all the necessary figures and solutions to each of the following problems. 1. Find the area of…

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Q: (c) SUPPLY RATE When the price of a certain commodity is p dollars per unit, the manufacturer is…

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Q: dx sinx+cosx

A: Follow the procedure given below.

Q: 1-x2 2 dy dx -1 J-V1-x² (1 + x² + y?)²

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Q: Distinguish First Derivative of a Parametric Equation from Second Derivative of a Parametric…

A: The given problem is solved below in detail.

Q: dy cot X Cos X Sin x +y=

A: The given DE is: cot x dydx+y=cos3xsin x⇒dydx+ycot x=cos3xsin x1cot x⇒dydx+(tan x) y=cot…

Q: Evaluate the following indefinite integral. dt t In(t) Note: Don't forget your C! And be sure to use…

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Q: Suppose that f(z, y) – e ¯4r² - 4y² - z + 2y Then the maximum is

A: The given function is: f(x,y)=e-4x2-4y2-x+2y Here,…

Q: Cassandra has the following information about f(x) and g(x): f(æ) = x →4 - 4, lim g(x) = 6. x →4 lim…

A: This is a problem related to limit. Based on the limit properties we will answer the question. As…

Q: Evaluate [², dx V4-x2 2.

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Q: Construct YOUR OWN example of how to determine the derivative of a given function and the process…

A: To write an example to how to find out the derivative and anti derivative.

Q: 3. Cylindrical Method a. y = 9 – x2,y = 0, about the x – axis b. y = Vx,y = x, about x – axis

A: Given

Q: (4x – 5y) lim (x,y)→(1,1) 5x² – 7y O -1/2 O 1/2 Limit DNE

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Q: find dy for ee Sin (メ+34) dx

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Q: x dy + ५ ax X cost d x dy 6- -2 ५

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Q: (B) Define the integral domain ring. Is the product of integral domain rings also an integr domain?

A: Integral domain: Integral domain is nontrivial ring with unity, containing no divisor of zero.

Q: 5. Determine the series converges, if so, Find its cum. whe ther K-1 a. k 1

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Q: Cnudan a pundre uuofree shrse trces nre prrabolae le » k).prrabolae ly - k). and kyyorobolne g = k).…

A: To find the quadratic surface whose traces are parabola(x=k), parabola(y=k) and hyperbola(z=k).

Q: (a) Use the trapezoidal rule to approximate the integral. | (4x° + 4) dx = - 1 (Round the final…

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Q: y"+y'=t ; where y(0)=1 and y'(0)=-2||

A: Here, the given DE is: y''+y'=t Taking Laplace transform on both the side:…

Q: recelve a star on the Hollywood Walk of Fame. 8. Kobe Bryant is a superstar player of Chicago Bulls.…

A: Negation

Q: 1 dx -1 1+ 3x²

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Q: sin(h) Evaluate: lim h →0 4h

A: Evaluating the limit with the help of standard limits.

Q: Consider the function: f(x) = 5x* – 2x³ + 3 Show that there is a value a e [0,2] such that f (a) =…

A: This question is based on continuity of function.

Q: Let f R R be continuous and let F be an antiderivative of/. If F) dr = 0 for some k > 1, then xf (x)…

A: This is a problem of integration. Based on the general formula and concept we will answer.

Q: dy =-2x tan y, 1- y(0) = 1/2. dx 2- 2 ydx CSOS 3- e*dx-ydy 0, y(0) = 1

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Q: Evaluate dx -31 x a,

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Q: Verify if y = 2eX + x - 1 solves v' = x -v |

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Q: Enumerate and explain the Four Second Partial Derivatives of the Partial Derivative of z with…

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Q: -2 Evaluate dx ех

A: The objective of the question is evaluate the definite integral.

Q: Evaluate the integral: 2T So * cos? (0)d0 *Input answer as decimal round-off to 2 decimal places

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Q: Solve the given DE: dy e* – 2x cos y eу — хx2 sin y' dx ||

A: Differential equations is solved.

Q: 8. Evaluate * y" – 3y' + 2y = e3t ; y(0) = y'(0) = 0 e2t -e3t + 2 et 23t -e2t + 2et 2 O A. e3t -e2t…

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Q: Evaluate the following indefinite integral. dx

A: Here is the solution

Q: Suppose that 10 grams of the 1 plutonium isotope Pu239 was released in the .Chernobyl nuclear…

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Q: |+ 3t -dt 11t Simplify the integrand by dividing eac .5 |+ 3t -dt = 11t |dt Type an exact answer.)

A: Given:∫1+3t511tdt

Q: Evaluate the integral: *Input answer as decimal round-off to 2 decimal places.

A: Given problem:-

Q: This question is about the function f(8) = (0 – 3) cos(@). (a) Explain why the graph of f lies on or…

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Q: Find the volume of the solid generated by revolving the area bounded by the given curves about the…

A: Given; x + y = 5      ,    y = 0   ,  x = 0 Volume (V) = ? Rotated about y = 0