calculus 2 find the derivative Assignment | Essay Help Services

Math 210
Assignment 1 (sections: 7.2, 7.3, 7.6, and 7.7)
Exercise 1: find the derivative of the following.
1)
2)
3)
4)
5)
6)
7) √
8)
Exercise 2: find the following integrals.
1) ∫
2) ∫
3) ∫
4) ∫
5) ∫
6) ∫
Exercise 3: find the derivative of y.
1)
2)
3)
4)
5)
Exercise 4: find the following integrals.
1) ∫
2) ∫ √
3) ∫ √
4) ∫
5) ∫ √
6) ∫
Assignment 2 (sections: 8.1, 8.2, and 8.3)
Exercise 1: use integration by parts to evaluate the following integrals.
1) ∫
2) ∫
3) ∫
4) ∫
5) ∫
6) ∫
Exercise 2: evaluate the following trigonometric integrals.
1) ∫
2) ∫
3) ∫
4) ∫
5) ∫
6) ∫
7) ∫
8) ∫
Exercise 3: use trigonometric substitution to evaluate the following integrals.
1) ∫ √
2) ∫ ⁄
3) ∫√
4) ∫√
5) ∫
6) ∫ √
Assignment 3 (sections: 8.4 and 8.7)
Exercise 1: decompose the following rational expressions into partial fractions in terms of constants A, B…etc. (do not evaluate these constants).
1)
2)
Exercise 2: Use partial factions to find the following integrals.
1) ∫
2) ∫
3) ∫
4) ∫
Exercise 3:
a) Find the partial fractions of :
b) Use an appropriate substitution to Deduce
∫
Exercise 4:
a) Find the partial fractions of:
b) Deduce the nature of convergence of ∫
Exercise 5: for each of the following improper integrals, determine its type then calculate it and deduce its nature of convergence.
1) ∫
2) ∫
3) ∫
4) ∫
Exercise 6:
a) Evaluate the following improper integral and deduce its nature of convergence ∫
b) Show that for any
c) Deduce the nature of convergence for
∫
Exercise 7: investigate the convergence of the following improper integrals by using comparison tests.
1) ∫ √
2) ∫
3) ∫
4) ∫
5) ∫
6) ∫√
Assignment 4 (chapter 10)
Exercise 1:
1) Find the limit as n goes to of the sequence whose nth term is
( )
2) Deduce the nature of convergence for the following series
Σ( )
Exercise 2: verify that each of the following series is divergent.
1) Σ
2) Σ ( )
Exercise 3: find the sum for each of the following series.
1) Σ
2) Σ
3) Σ √ √
4) Σ
Exercise 4:
1) Show that : ∫
2) Use part (1) to determine whether the following series is convergent or divergent Σ
Exercise 5:
1) Show that the improper integral ∫
2) Use part (1) to determine whether the following series is convergent or divergent Σ
Exercise 6: for each of the following, say whether it converges or diverges and explain why.
1) Σ √ Σ
2) Σ √ Σ
3) Σ Σ
4) Σ Σ
1) Σ Σ
2) Σ Σ √
Exercise 6 : Find the interval of convergence for each of the following the
Power series.
1) Σ
2) Σ
3) Σ
Exercise 7:
Find the Taylor series for the function centred at a=0 and hence that for ( )
Assignment 5 (chapter 11)
Exercise 1:
a) Find the Cartesian equation of the circle and sketch its curve.
b) Study the symmetry of and sketch its curve.
c) Find the area of the region in the polar coordinate plane that lies outside the cardioid of and inside the circle .
Exercise 2:
a) Find the Cartesian equation of the circle and sketch its curve.
b) Study the symmetry of and sketch its curve.
c) Find the area of the region in the polar coordinate plane that lies between the curve of and the circle
Exercise 3: find the lengths of the following curves.
1) ,
2) ,
3) √ √