MATH 1B Midterm: MATH 1B Harvard Exam1 review
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1 improper integrals: two of your young classmates are having some trouble with improper. 0 f (x) dx where f is de ned, positive, integrals. They are discussing r and bounded on [0, ) and limx f (x) = 0. She reasons that if f is positive then then the accumulated area keeps increasing, even if only by a little bit, so we can"t get anything other than in nity since r b. 0 f (x) dx increases with b and we need to let b go to in nity. Amani, on the other hand, is convinced that if limx f (x) = 0, then. After all, he reasons, the rate at which area is accumulating is going to zero. Explain very clearly the errors each of them are making. There is really not enough information given about r .
