Q2) Solve the BVP utt = Uxx ux(0,t) = 0 u(x,0) = 0,_ u₂(x,0) = f(x) = {100 0 0 01

Q: f(x + h) – f(x) f'(x) = lim h-0 %3D h bsnd Diffeentinble A) 7xh2 B) 9x2h C) 5x2 D) 9x2 5) Given (x")…

A: Given that: 4. f(x+h)-f(x)=9x2h+7xh2+5h35. (xα)'=αxα-1

Q: FIND M'(3) = Page 2 of 4 -1 6 2 g(x) • F(x) LET M (x) = F (g(x)) AND V(x) = 9 (f(x)) 6 FIND V'(3) =

A: Step 1: Step 2: Step 3: Step 4:

Q: x-1 pose g(x) Find the value of x in the interval 1, o0) where g(x) takes on its maximum value.

A: Given query is to find the the value of x where g(x) will be maximum.

Q: g(0) -- y = 3

A:

Q: d. y= x² + y x + cos y

A:

Q: not Show that ([0,1]_is in the l' metric d (fig)= (51f6)-96) ³d x) ² fumpluts

A: The given set is X = C[0,1] and the metric defined on X is L2 metric which is defined as  df, g =…

Q: Determine the interval of existence and uniqueness without solving

A:

Q: prove that P(X)=P(X|F)P(F) + P(X|F')P(F')

A: