Find the derivative of In(3t³ – 2t + 1) and then calculate S; + 3 dt (use integration by recognition). ar-2t+1

Q: Compute the derivative of f(t) = (3t2 + sin t, cos3 t + 8t2, 5tan t) relative to t.

A: d(u+v)/dt=  du/dt + dv/dt

Q: Given f(x) = 8x3 + In(x – 1). Estimate the value of f(2.01) using differential. %3D

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Q: У (2ху + 1)dx — хӑу %3D 0 ||

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Q: Calculate the derivative e12x d In (t)dt dx using Part 2 of the Fundamental Theorem of Calculus.

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Q: Determine an integrating factor and solve the followir xdy-ydx-(1-x')dx = o 1.

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Q: In the integration What is the implicit derivative of u? V9-4x² a. du = 2dx %3D b. du = * c. du =-…

A: dx9-4x2=dx32-2x2 Put, u=2x⇒dudx=21⇒du=2 dx

Q: ) Evaluate (3t+ 5) cos dt using integration by parts. 4.

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Q: Take a look at the derivative of the integral (4t² – 2t + 7) dt. d - dx -4

A: topic - derivative and integration

Q: Find the simplest integrating factor u(x) of - xy' = (8x + 9)y + x In(x). µ(x) = %3D

A: As the given equation is an first order differential equation ,we can find integrating factor.

Q: Take a look at the derivative of the integral * S (6t2 – 5t + 2) dt. (6t² dr Evaluate the…

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Q: Use partial differentiation to find the derivative of the implicit function dy (3x'y-1)+ 7xy = 9…

A: We will use the given formula to solve this question.

Q: Find the differential of the function. z = 3t - = zp

A: Differentiate the function: - Differentiation is that the quantitative relation of a small amendment…

Q: Verify the statement by showing that the derivative of the right side is equal to the integrand on…

A: We will find the derivative of right side. By showing this derivative equal to integrand the…

Q: Find the value of dx (7x – 2)° If the integral diverges, give "oo" as your answer. -

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Q: Find the indicated derivative. dp for p q² + 2 5q – 3 %3D dq dp dq II

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Q: This is a linear DE. If arranged to its form, what is the integrating factor? * xdy ニ

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Q: Show that the integral -21/RC e dt has the value

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Q: P (a, b) = So -at² _e-bt2 dt %3D t2

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Q: Find the derivative of In(3t3— 2t + 1) and then calculate  ∫ (9t2-2/3t3-2t+1) + 3 dt (use…

A: Given         ln(3t3-2t+1)

Q: Calculate the derivative 10z d dz In (t)dt using Part 2 of the Fundamental Theorem of Calculus.

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Q: Exercise 10. Find the derivative d 7x (* + 2) dt dx

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Q: Use Part 1 of the Fundamental Theorem of Calculus (and properties of definite integrals and the…

A: Solve the following

Q: Use differentials to approximate V36.1. 3.

A: Consider y = root x.Let take x = 36 and delta x = 0.1.Find delta y as follows.

Q: Use Part 1 of the Fundamental Theorem of Calculus to find the derivative of the function. rtan(x) 5t…

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Q: In integrating the function f(3x + 5)(cos) dv using integration by parts, what would you choose for…

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Q: A 1125 m³ open-top rectangular tank with a square base x m on a side and y m deep is to be built…

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Q: Use Part 1 of the Fundamental Theorem of Calculus to find the derivative of the function. (The…

A: Solution :-

Q: Find the total differential z = 5x3y2

A: The given function is z=5x3y2. Total differential: Let z=f(x,y) be continuous on an open set S. Let…

Q: Calculate the derivative 12x d dx In (t)dt using Part 2 of the Fundamental Theorem of Calculus.

A: follow next step

Q: Use an integrating factor to solve the IVP y'+ytan x = cos x, with IC (x, , Yo) = (0,7), %3D and…

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Q: (b) Use the total differential dz to approximate Az. dz = X

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Q: (§5.5, Q34) Calculate the derivative d dæ ), Vi dt.

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Q: 3. Verify the statement by showing that the derivative of the right side is equal to the integrand…

A: Since you have asked multiple questions in a single request, we would be answering only the first…

Q: 4. Compute dx S in two ways and verify that the answers agree.

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Q: "Differentiate both sides of the equation V = Tr*with respect to t AP (using the chain rule on the…

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Q: In the integration What is the implicit derivative of u? V9-4x* a. du = 2dx b. du = * c. du =– 2dx…

A: Implicit differentiation of integral

Q: Find the derivative. |4t +5 dt O A. V4x+5 O B. V4x+5 - 5 2 OC. V4x +5 OD. (ax + 5)/2

A: It is given that, y=∫0x4t+5 dtWe have to find the derivative.

Q: Use Part 1 of the Fundamental Theorem of Calculus to find the derivative of the function.  g(x)=…

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Q: Find Zxx=Zyy=Zxy=

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Q: Find the integration inner product on C[-4, 3] of the given functions. f(x) = 16x g(x) = 2x?

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Q: Find the total differential of z = In (2x – 3y).

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Q: What value of x > -1 maximizes the integral / t²(3 – t)dt?

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Q: 2) Find second derivative d'F/dt? of 312-2 F? = 13 and find it at (t,F) = (-1,2)

A: We have to find the required second derivative at the given point.

Q: Calculate the derivative 26 dt d (6£4 dx using Part 2 of the Fundamental Theorem of Calculus. 26 dt…

A: According to the fundamental theorem o calculus:

Q: 1. Evaluate S Vx3 +1 dx dy by reversing the order of integration.

A: Given:

Q: In the integration ∫dx/√9-4x^2, What is the implicit derivative of u? a. du= 2dx b. du= dx/2 c.…

A: To find: The implicit derivative of u. Given: The integration is ∫dx9-4x2. Calculation: The…

Q: Calculate the derivative 27 dt d da using Part 2 of the Fundamental Theorem of Calculus. d dx 27 dt…

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Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.