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- Use Simpson's 3/8 rule to compute the approximated solution where f (x) = 1/Cosx + 4 defined at the interval (1,4.5) and n = 7Jesaki Inc will sell N units of product after spending $x thousand in advertising, as given by N= 66 x−x2. Use differential approximations to estimate the increase in sales that will result by increasing the advertising budget from $10,000 to $10,589. Round to the nearest integer. $Suppose a spherical balloon grows in such a way that after t seconds, its volume V is given by V = 4 t1/2 cm3. After 100 seconds the radius of the balloon is r = 2.121568836 units? sec cm cm^2 cm^3 cm/sec cm^2/sec cm^3/sec . How fast is the radius changing after 100 seconds? dr dt = units? sec cm cm^2 cm^3 cm/sec cm^2/sec cm^3/sec
- Suppose U solves the heat equation on the real lineUt = 4Uxx, x ∈ Rwith initial valueU(x, 0) = (4, x ≤ 02, x > 0.(i) Use the Fourier-Poisson formula to give an explicit expression for the solutionU.(ii) Describe the qualitative behaviour of U in this case as t → ∞ and plot outthe solution at several instants of time to explain your answer. What is the limitof U as t → ∞?EVALUATE THE FOLLOWING DIFFERENTIAL EQUATIO0N USING BERNOULLI'SAssume that your computer completes a 5000 equation back substitution in 0.005 seconds. Use the approximate operation counts n2 for back substitution and 2n3/3 for elimination to estimate how long it will take to do a complete Gaussian Elimination of this size. Round your answer to the nearest second.
- calculate....along the curve curve in the first octant given by x^2 + y^2 + z2 = 4, (x − 1)2 + y^2 = 1.Integrate from f(x) = x4 from 0 to 1 by (Trapezoidal Rule) with h = 1, h = 0.5, h = 0.25 and estimate the error for h = 0.5 and h = 0.25 by (Error Estimation by Halving h).for the second question, could u plz explain in detail why the upper and lower bound change in this way (see image 1)? And the fubuni theorem tells us the change of order of dxdy to dydx won't change the upper/lower bound (see image 2), why this bound changing doesn't need to follow the fubuni theorem?
- Give the linear approximation L(x) of tan(πx) in x=1/4soultions from previous is COV(x,y)=3, corraaltion = pxy=1/2,A rectangular plate with insulated surface is 10 cm. wide and so long compared to its width that it may be considered infinite length. If the temperature along short edge y = 0 is given u(x,0) = 8 sin(px/ 10) when 0 <x <10, while the two long edges x = 0 and x = 10 as well as the other short edge are kept at 0o C, find the steady state temperature distribution u(x,y).