In exercises 1-6, evaluate the integral.
![1846_Evaluate the integral.png](https://secure.tutorsglobe.com/CMSImages/1846_Evaluate%20the%20integral.png)
7. Determine whether the improper integral is convergent or divergent. If it converges, find it value.
![1055_Evaluate the integral1.png](https://secure.tutorsglobe.com/CMSImages/1055_Evaluate%20the%20integral1.png)
8. Find the length of the curve, y = 2x3/2, from x = 0 to x = 1
In exercises 9 and 10, determine whether the sequence converges or diverges. If it converges, find the limit.
![1557_Evaluate the integral2.png](https://secure.tutorsglobe.com/CMSImages/1557_Evaluate%20the%20integral2.png)
In exercises 11-14, determine whether the series converges or diverges. Indicate the test(s) that you use to support your conclusion.
![705_Evaluate the integral3.png](https://secure.tutorsglobe.com/CMSImages/705_Evaluate%20the%20integral3.png)
15. Find the values of x for which the series converges. Check endpoints.
![173_Evaluate the integral4.png](https://secure.tutorsglobe.com/CMSImages/173_Evaluate%20the%20integral4.png)
16. Find the first four terms of the Taylor series of f(x) = ex at a = 1.
17. solve the differential equation.
![1780_Evaluate the integral5.png](https://secure.tutorsglobe.com/CMSImages/1780_Evaluate%20the%20integral5.png)
19. Solve the initial-value problem.
y'' + 6y' + 9y = 0 , y(0) = 2 , y'(0) = 1
20. Find the general solution of the nonhomogeneous differential equation, y'' + 3y' - 10y = e4x
Suggestion: use the method of undetermined coefficients.