2 Multiple choice (1) Suppose that f(x) is continuous at [0,1] int _(0)^1f(x)dx= A lim _(narrow infty )sum _(k=1)^nf((2k-1)/(2n))(1)/(2n) B lim _(narrow infty )sum _(k=1)^nf((2k-1)/(2n))(1)/(n) C. lim _(narrow infty )sum _(k=1)^2nf((k-1)/(2n))(1)/(n) D. lim _(narrow infty )sum _(k=1)^2nf((k)/(2n))(2)/(n) (2) If lim _(narrow infty )((n^2+1)/(n+1)-an-b)=0 then A. a=1,b=0 B. a=1,b=1 C. a=1,b=-1 D. a=0,b=1

(1) The correct answer is A. Explanation: The integral can be approximated using a Riemann sum. In this case, the Riemann sum is given by , where is the number of subintervals, represents the th subinterval endpoint, and is the width of each subinterval.(2) The correct answer is C. Explanation: To find the values of and , we need to simplify the expression . By dividing the numerator and denominator of the fraction by , we get . As approaches infinity, approaches 0, so the expression simplifies to . For this limit to be equal to 0, we must have and .