Suppose that we need to find the solution of y" = y², y(a) = 0, y(b) = 2 by finite difference method. The 4-th derivative of the exact solution has Maximum M = 2 in the interval [a, b]. The computer has round-off error e = 5 * 10 5. If we choose the value of h very small, the round-off error will be high, and if we choose h high, the truncation of error will be high. The optimal value of h that reduces both error kinds is O a. 0.186121 O b. 0.124467 O c. 0.104664 O d. 0.0699927

Q: Let f(x)=x+(1−x)^(1/2) Find the local maximum and minimum values of f using both the first and…

A: For local maxima or minima:The first derivative test is f'(x) = 0The second derivative test…

Q: Show that Costy+ Co5' (-x ) = TT.

A: To show that the given identity is true,

Q: Please find the requested derivative of the following functions. s²-4st+t² = 4, find 25 ds dt - ds…

A:

Q: O The graph of f(x)=2r²+2r-12 is shown alongside. a Find f'(x). b Hence find the point where the…

A: Given: y=fx=2x2+2x-12 For a functiony=fx at any pointx,y gradientm of tangent is given by m=dydx|x,y…

Q: b) f(x)=√x - √x c)

A:

Q: (2) x'+4xy -3 y – 2021 = 0

A:

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.