**203 S Calculus 2**

**[numbers in square brackets are marks]**

**(1) Perform the following integrals:**

**[5] ( a)**

**[5] ( b)**

**[5] ( c)**

**[5] ( d)**

**[5] ( e)**

**[4] ( f)**

**(2) Calculate the following
limits:**

**[4] ( a)**

**[4] ( b)**

**(3) Determine if the following
integrals converge or diverge:**

**[4] ( a)**

**[4] ( b)**

**[6] (4a) Find the volume of the solid of revolution obtained
by rotating the region bounded by the curvesandabout the x-axis. Indicate which
method you are using.**

**[4] (4b) Find the area of the
region.**

**[4] (5) Findand
simplify:**

**(6) Determine whether the
following series converge or diverge. State the test used and show that
the conditions of the test have been met.**

**[5] ( a)**

**[5] ( b)**

**[5] ( c)**

**[5] ( d)**

**(7) Determine whether the
following series as absolutely convergent, conditionally convergent, or
divergent.**

**[5] ( a)**

**[5] ( b)**

**[6] (8) Find the interval of convergence for:**

**[5] (9) Find the first
three non-zero terms of the Taylor series forabout.**