Calculus. Finding the solutions for a given assignment. (Essay Sample)

Provide solution to the following questions:
1. Evaluate the following:
 
Using integration by parts
U = x dudx=1 , therefore du =dx
dv =sin3x dx v =- 3cos3x
= vu -vdu
=-x3cos3x+13cos3x dx
=-x3cos3x+19sin3x +c
2. If, then for what value of α is A an identity matrix?
lefttopto find the determinant of matrix A
cos2α - sin2α =1 but cos2α +sin2α =1
cos2α - sin2α = cos2α +sin2α
0 = 2sin2α , sin2α = 0 α = o0 0r α =3600
3.  The line y = mx + 1 is a tangent to the curve y2 = 4x .Find the value of m.
y=2x12
dydx=x-12 at the point p(x ,y)
So the gradient at p(x ,y) = x-12
x-12 = m
4. Solve the following differential equation: (x2 − y2) dx + 2 xy dy = 0.
x33-xy2+xy2+c=0
x33+c=0
x3+3c=0
x3+k =0
5. Solve system of linear equations, using matrix method.
x − y +2z =73x +4y −5z =−52x − y + 3z