1) How to solve the IBVP Utt=c²Uxx subject to the following conditions Ux(0,t)=0= Ux(1,t) U(x,0)= cos2πx , Ut(x,0)= -2πcosπx where x E [0,1]

2) Utt=c²Uxx Ux(0,t) = 0 = Ux(1,t) , t>1 U(x,0)=0, Ut(x,0)=-1 when 1/4<x<3/4 =0 otherwise Plz help

Find a formula for a function f that satisfies the following conditions.

5. (5 points Recall that by definition, a linear transformation must satisfy the following conditions: (I) T[X+Y] = T[X] +T[Y] (II) T[aX] = aT[X] 17 [CD] - ( 1 ) and T[()] - ( - , then evalute [(-1)].

Write eqaution of rational function, f(x), that satfies the following conditions:

f(x) < 0 throughout the domain of the function

The function has restrictions at x=-2 x=5