Assignment:
Q1.) For the arithmetic sequence {-10,-2,6,14,}, find:
a.) a recursive rule for the nth term
b.) an explicit rule for the nth term
Q2.) For the geometric sequence {512,256,128,64,...}, find:
a.) a recursive rule for the nth term
b.) an explicit rule for the nth term
Q3.) Determine whether each of the following sequences converges or diverges. If it converges, find its limit.
a.) a= (5+2n)/(n^2)
b.) a= (-1)^n(1.001)^n
Q4.) Which grows faster as x approaches infinity, lnx or x^3?
a.) lnx grows faster b.) x^3 grows faster c.) they grow at the same rate
Q5.) Which grows faster as x approaches infinity, (x-4)^3 or 2x^3+lnx?
a.) (x-4)^3 grows faster b.) 2x^3+lnx grws faster c.) they grow at the same rate
Q6.) Evaluate the integral from 0 to infinity of (dx)/((1+x)(square root of x)) or state that it diverges.
Q7.) Use partial fractions to evaluate the integral of (20x+16)/(x^2+3x+2)dx.
Provide complete and step by step solution for the question and show calculations and use formulas.