Provide solution to the following questions:

- Evaluate the following: ∫xsin3xdx

This question requires integration by parts

Let u=x and dv/dx =sin (3x)

du=x dx=1

But

- The line y = mx + 1 is a tangent to the curve y
^{2}= 4x .Find the value of m.

Substitute y=mx+1 in =4x

= 4x

Expanding = 4x

+1+2mx-4x=0

+x(2m-4)+1=0

The tangent touches the curve at one point hence the roots are equal. Therefore, discriminant =0

-4((1) = 0

+16-16m-=0

16-16m=0

16=16m

M=1

- Solve the following differentialequation:(
*x*^{2}−*y*^{2})*dx*+ 2*xy dy*= 0.

Te integrating factor of the equation is

- Solve system of linear equations, using matrix method.

*x* − *y* +2*z* =7

3*x* +4*y* −5*z* =−5

2*x* −* y* + 3*z* = 12

Hence

X=2

Y=1

Z= 3

Reference

Chirgwin, B., & Plumpton, C. (2016). *A course of mathematics for engineers and scientists*. Elkins Park: Pergamon Press/Elsevier Science.

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