Chapter 10.1, Problem 15E

Explain the key points of 11.3.6 and prove it

Explain the key points of 11.3.3

explain of logical relationships of (11.1.1), (11.1.2), (11.3.4), (11.3.6)

Prove 11.1.2

39. (a) Show that Σeak converges for each α > 0. (b) Show that keak converges for each a > 0. k=0 (c) Show that, more generally, Σk"eak converges for each k=0 nonnegative integer n and each a > 0.

#3 Find the derivative y' = of the following functions, using the derivative rules: dx a) y-Cos 6x b) y=x-Sin4x c) y=x-Cos3x d) y=x-R CD-X:-:TCH :D:D:D - Sin f) Sin(x²) (9) Tan (x³)

mate hat is the largest area that can be en 18 For the function y=x³-3x² - 1, use derivatives to: (a) determine the intervals of increase and decrease. (b) determine the local (relative) maxima and minima. (c) determine the intervals of concavity. (d) determine the points of inflection. b) (e) sketch the graph with the above information indicated on the graph.

use L'Hopital Rule to evaluate the following. a) 4x3 +10x2 23009׳-9 943-9 b) hm 3-84 хто бу+2 < xan x-30650)

Evaluate the next integral