b) write an expression for the position in terms of time t, use c (lower case) to denote constant of integration.

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Q: Define the term“constant integration”?

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Q: / Use the Newton - Raphson method to estimate the root of f(x) = e* - x , employing an initial guess…

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Q: Describe the change in accuracy of dz as an approximation of ∆z as ∆x and ∆y increase.

A: Given , z=fx,yWe do dz using the partial derivates zx & zy .So , dz=zx.dx & zy.dywhere zx…

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

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Q: 10. t(x) = Vx+3+4

A: Given function t(x)=x+3+4

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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: Use a linear approximation (or differentials) to estimate the given number. V 99.4

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Q: 1 dx = +C (x+1)² X+1

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Q: Use the Power Rule to compute the derivative.

A: To compute the derivative using using power rule: ddtt-3t=4. Solution: Power rule of differentiation…

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Q: to***) dx . Refresh your integrating skills and evaluate

A: Answer

Q: f '(x) = 10x9,  what is f(x)? (Use C for the constant of integration.)

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Q: Use a linear approximation (or differentials) to estimate the given number. 99.8 9.9

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Q: Find the derivative. t6 d 5 du dt a. by evaluating the integral and differentiating the result. b.…

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Q: Use the Fundamental Theorem of Calculus, Part 1 to find the derivative: d •√x (t² + Int)dt dx Sa

A: First I have written the Fundamental theorem of Calculus and using it for given problem and find the…

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

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Q: Find a root of an equation f(x) = cos(x) - − using Newton Raphson method

A: Let us start solving the problem step by step  Given  Cos(x)-(x/6)=0 Let f(x)= cos(x)-(x/6) We will…

Q: If  f '(x) = x4,  what is f(x)? (Use C for the constant of integration.)

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Q: Use the General Power Rule, Exponential Rule, or the Chain Rule to compute the derivative.

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Q: 2x-x² dx

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Q: Find the linearization of the function f(x) = sin(x) at a = π and use it to approximate the number…

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Q: Find the antiderivative of x/sqrt (x2+1) and verify it by differentiation?

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Q: Use the Power Rule to compute the derivative.

A: The power rule of derivative is given by dxndx=nxn-1 Using the above rule: dt-2/5dt=-25t-25-1…

Q: Use Newton's Method to approximate the zero(s) of the function f(x) = x' +4x +1

A: f(x) = x5 + 4x + 1 Basic formula for Newton's Method is: xn+1 = xn - fxnf'xn f'x = 5x4 + 41 + 0 =…

Q: S 3p? tan p dp

A: To integrate.

Q: If f'(x) = 4x°, what is f(x)? (Use C for the constant of integration.) f(x) = %3D

A: It is known that ∫xn dx=xn+1n+1+C provided n≠-1. Given that f'x=4x3. Integrate as follows.

Q: For what function P is the integrating factor α(x) equal to ex?

A: Here the given integrating factor

Q: [ to y²-Xy flo dy 2

A: 1st we will use substitution and then integration by parts   ∫u.v dx=u∫v dx -∫dudx∫v dxdx

Q: If f'(x) = 5x*, what is f(x)? (Use C for the constant of integration.) f(x) =

A: To find the integration

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

A: To find the derivative of the h(x) using fundamental theorem of calculus part 1.

Q: 30. Based on the R output, the most appropriate coefficient to describe the relationship between…

A: The R-output of Pearson's correlation and Spearman's correlation is given.

Q: la y is not measurable. Wan

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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…

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Q: find the following integration:-

A: “Since you have asked multiple question, we will solve the first question for you. If you  want any…

Q: Use the Newton-Raphson method to find the root of f(x) = lnx+x in the interval [0.5,1] with an…

A: Mathematical methods used to solve equations or evaluate integrals or solve differential equations…

Q: Evaluate the derivative So (3t² – 2t +1) dt. -

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Q: dx = +C (x+1)² X+1

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Q: Which formula gives the x-coordinates of the maximum values for y = cos(x)?

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Q: A total cost function (in dollars) is given by C(x) = 116 + 3x + 0.37x. Use differentials to…

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Q: Find the root using newton raphson method for f(x) = sin(x) − x²

A: Given function is f(x)=sin(x)-x2 From the given equation, it is clear that 0 is one of the root of…

Q: Find the root of x² - 1000 = 0 using Newton's law of approximation

A: We have to approximate the root of x7-1000=0 now we have f(x)=x7-1000,  f'(x)=7x6 Newton's law of…

Q: Find y′ by implicit differentiation. e^(x/y)=4x−2y y'=?

A: To calculate the value dy/dx from the provided implicit differentiation e(x/y)=4x-2y. Now,…

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A: Given that r=4 T=4z+3sin4(πz) Apply the quotient rule to take derivative We know that the derivative…

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Q: Perform the Integrations sin(r)dt

A: To Find : ∫sin(t)dt

Q: What is the integrating factor of y' - 2xy x?

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Q: If f'(x) = x*, what is f(x)? (Use C for the constant of integration.) %3D f(x) = %3D

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Q: Find y" by implicit differentiation. 9x2 + y2 = 4 y" = %3D

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