Math subjective test 2
Provide solution to the following questions:
- Evaluate the following: ∫xsin3xdx
This question requires integration by parts
Let u=x and dv/dx =sin (3x)
- The line y = mx + 1 is a tangent to the curve y2= 4x .Find the value of m.
Substitute y=mx+1 in =4x
Expanding = 4x
The tangent touches the curve at one point hence the roots are equal. Therefore, discriminant =0
-4((1) = 0
- Solve the following differentialequation:(x2 − y2) dx + 2 xy dy = 0.
Te integrating factor of the equation is
- Solve system of linear equations, using matrix method.
x − y +2z =7
3x +4y −5z =−5
2x − y + 3z = 12
Chirgwin, B., & Plumpton, C. (2016). A course of mathematics for engineers and scientists. Elkins Park: Pergamon Press/Elsevier Science.