Consider the function f(x) = *+7. 4 In this problem you will calculate | + 7) dx by using the definition f(x) dx = lim |E f(x;)Ax n00 i=1 The summation inside the brackets is R, which is the Riemann sum where the sample points are chosen to be the right-hand endpoints of each sub- interval. Calculate R, for f(x) = * +7 on the interval [0, 4] and write your answer as a function of n without any summation signs. R, = lim R, = n-00

1) Find the intervals of increase and decrease for f(x) = t³ + 3t² + 1. (Use interval notation when writing intervals for the whole test.)

3. Consider the function for x +0 f(x) 1 for x = 0. (b) Divide the interval [-1, 1] into 2n parts. Approximate the area under the curve by rectangles, using... i. ..the left endpoint on subintervals of [-1,0] and the right endpoint on subin- tervals of [0, 1].

(1 point) Evaluate 2 6²₁ f(x) dx = = [ 2 f* f(x) dx, where f(x)= = [7r5, 0