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- If you travel 300 miles on the first day and then drive v miles per hour for t hours on the second day, then the total distance traveled over the teo-day period is given by d=300+vt miles. Use a formula to express v as a function of d and t for this two-day event.a) Estimate the length of this arc with the length of the line segment joining the endpoints of the arc. y=3x^(3/2)-1 over the x -interval [0, 4]. b) Use integration to find the true length of this arc.f(x)=3-x, p=6, expand the function into its sine representation and evaluate f(1) of the series at n=2.Use 2 decimal places.
- Note: (D) =Diverge (C) =ConvergeUse linear approximations to estimate the following quantitie. Choose a value of a to produce a small error. ln 1.05Integrate the following functions analytically and numerically. Use the Trapezoidal method to numerically integrate with n=4. Calculate the error against the analytical results.
- Use the simple fixed-point method to locate the root of: f(x) = sin(x)cos(x) − x + 1 Use the initial guess of x0 = 1.5 and iterate until ϵa ≤ 0.15%.Use the Secant Method to approximate the positive root of 2x^2-sin^-1x=0. Sketch the graph of the corresponding function to find an appropriate initial estimate x-1 and x0.Find the linear approximation of f(x)=cos(x) at x=3π/4 and use it to approximate cos(137∘). Give your answer rounded to four decimal places. For example, if you found cos(137∘)≈0.86612, you would enter 0.8661.
- Use the series representation of the function f to find the attachment. f(x), if it exists .f(x) =( sin x)/ xDetermine whether the following statement is true or false, and explain why. Newton’s method converges as long as there is a real root and the function is differentiable.Apply Newton’s method twice to approximate 7^(1/3) . Use the initial approximation xsubscript0 =2
