Problem # 6 A farmer has 2400 ft of fencing and wants to fence off a rectangular field that borders a straight river. He needs no fence along the river. What are the dimensions of the field that has the largest area? Problem # 7 Calculate lim (1+ sin 4x ) cotx Problem # 8 Consider the following theorem. Theorem If f is integrable on [a, b], then ['A(x ) dx = lim \\Rx . )Ax where Ax = - a and x. = a + ix. n Use the given theorem to evaluate the definite integral. ( x 2 - 4x + 6 ) dx