Prerequisite to Laplace Transofrm

1. What is the derivative of f(x) = x^2?

• 2x

• x + 1

• 2x^2

• x

2. The integral of sin(x) with respect to x is:

• -cos(x) + C

• sec(x) + C

• -tan(x) + C

• tan(x) + C

3. What is the solution to the differential equation dy/dx = 2x?

• y = 2x + C

• y = 3x + C

• y = x^3 + C

• y = x^2 + C

4. The general solution of y' + y = 0 is:

• y = Ccos(x)

• b) y = Ce^-x

• y = Csin(x)

• y = Ce^(2x)

5. Which of the following is Euler's formula?

• a) e^(iθ) = cos(θ) + i sin(θ

• e^(iθ) = cos(θ) - i sin(θ)

• e^(iθ) = cos(θ) + θ

• e^(iθ) = 1 - i θ

6. What is the second derivative of f(x) = x^3?

• a) 6x

• x^2

• 6x^2

• 3x

7. The integral of e^x with respect to x is:

• a) e^x + C

• x^2e^x + C

• e^(x+1) + C

• e^x - C

8. What is the solution to the differential equation dy/dx = 3y?

• y = 3e^(x)

• y = e^(3y)

• y = Csin(3x)

• y = Ce^(3x)

9. The Laplace transform of f(t) = t^n is:

• s^n/n

• (n+1)!/s^(n+1)

• a) n!/s^(n+1)

• n!/s^n

10. What is the integral of 1/x with respect to x?

• sin(x) + C

• ln|x| + C

• x^2 + C

• log(x) + C