# Test for divergence integral test p series comparison

• Notes
• 2

This preview shows page 1 - 2 out of 2 pages.

Test for Divergence Integral Test p -series Comparison Test Limit Comparison Test Alternating Series Test Ratio Test Root Test Practice Problems: 1. Find the length of each curve: a) y = 1 3 x 3 / 2 - x 1 / 2 , 1 x 4 b) x 2 = y 3 , 0 x 8 c) x = t - 2 t 2 , y = 8 3 t 3 / 2 , 1 t 2 2. Solve the differential equation x + 1 y + y = 0. Draw a slope field and a few typical solution curves. 3. Solve the initial value problem y = x y 4 , y (0) = 2. 4. Sketch each parametrically defined curve, including a direction arrow. a) x = cos( t ), y = sin 2 ( t ), 0 t π b) x = t 4 - t 2 , y = t 2 , t 0 5. For the curve x = 5 - t 2 , y = t 3 - 6 t , do the following: a) Find dy/dx and d 2 y/dx 2 . b) Find an equation of the tangent(s) to the curve at the point (1 , 4). c) Find the point(s) on the curve where the tangent line is horizontal or vertical.
6. Test each series for convergence. Find the actual value of any convergent geometric series.
7. Test each series to see whether it is absolutely convergent, conditionally convergent, or divergent. a) summationdisplay n =1 ( - 1) n 3 n b) summationdisplay n =0 ( - 10) n n ! c) summationdisplay n =0 ( - 1) n n n + 5 d)