please help me solve these questions and please write them in a notebook for a better understanding of the solution. thank you

1 . Define each formula. Each formula means something different. Make sure your definitions are different. a. If ( x; ) AX i=1 b. lim If ( x ; ) AX n->oo ; =1 C. lim max AX; ->0 If ( x ; ) AX , 2. Express the limit as a definite integral on the given interval. lim 3i 1+ 1->0o - 1 n n 3. Use left endpoints with Ax = 1 to estimate the area under the graph of f(x) = x2 + 1 from x = 1 to x = 5. Write out the sum, do not evaluate the sum. 4 . If [of( x)dx =7 and [ f(x)dx = 6, find the value of [f(x)dx. 5. If g(x) = sin?(t)dt, find g'(x).Answers: 1. a. Estimates the area under the curve. b. Finds the exact area under the curve. c. Finds the exact area under the curve using different widths for the rectangles. 2. 3V; dx 11f(1)+1f(2)+ 1f(3)+1f(4) -1 5_ g'(x) = 2xsin2(x2) :PP"