Homework 13- Additional ExercisesProblems 1 Homework 13- Additional ExercisesProblems 1 Homework 13- Additional ExercisesProblems 1 & 2 regard the Integral Test (see section 11.3).Problems 3-5 concern Comparison Tests for infinite series (see section 11.4).Suppose f is a continuous, positive, decreasing function for x1 and that an=f(n). By drawing a picture, rank the following three quantities in increasing order:16f(x)dx,k=15ak,k=26ak(a) In the derivation of the Integral Test, it was established that whenever f is a continuous positive decreasing function for all x1 thenf(2)+f(3)+f(4)+dots+f(n)1nf(x)dxUse this result to show that k=1n1k1+lnn.(b) The harmonic series n=1+1n diverges, but very slowly. Use part (a) to show that the sum of the first million terms is less than 15 and the sum of the first billion terms is less than 22.