MAC 2311 Midterm: MAC 2311 FIU Exam 214k
15 Feb 2019
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Explain why f must have an inverse function. Then compute and simplify d dx tan 1(x) using the (f 1) theorem as done in class: [10pts] an circular oil spill is spreading at a rate of 500 square feet per hour when the radius is 100 feet. How fast is the radius increasing then: [10pts] compute limx + x2+2x x+1 x. Use l"hopital"s rule if / when possible: [15 pts] answer true or false. The domain of f is the same as the domain of f . d dx tan 1(x) + d dx cot 1(x) = 0. If f is continuous and has an inverse, then f 1 is continuous (on its domain): [10 pts] choose one of the problems below to do. Include enough comments and/or justi cations: state and prove the power rule (when n > 0 is an integer), show that d dx (cos(x)) = sin(x).
