Provide exact answers to the following, except when otherwise noted. (Recall that x = √ 2 is an exact solution to the equation x 2 = 2, while x = 1.414213562 is an approximate solution, and that you will not have access to calculators on exams.) 1. For what values of p does the series X[infinity] n=1 ln n np converge? 2. Show that if an ≥ 0 and X[infinity] n=1 an converges, that X[infinity] n=1 (an) 2 does too. 3. Show that if an ≥ 0 and X[infinity] n=1 an converges, that X[infinity] n=1 ln(1 + an) does too. 4. Show that if an ≥ 0 and X[infinity] n=1 an converges, that X[infinity] n=1 sin(an) does too.

You decide instead to take the train there. the train will take 135 minutes. convert this into hours and minutes.

Which number line correctly shows 0.8 + 0.3?

The equation shown below represents function f. f(x)= -2x+5 the graph shown below represents function g. which of the following statements is true? a. over the interval [2, 4], the average rate of change of f is the same as the average rate of change of g. the y-intercept of function f is less than the y-intercept of function g. b. over the interval [2, 4], the average rate of change of f is greater than the average rate of change of g. the y-intercept of function f is greater than the y-intercept of function g. c. over the interval [2, 4], the average rate of change of f is the same as the average rate of change of g. the y-intercept of function f is greater than the y-intercept of function g. d. over the interval [2, 4], the average rate of change of f is less than the average rate of change of g. the y-intercept of function f is the same as the y-intercept of function g.