MATH 120 Midterm: MATH 120 2016 Winter Test 1
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This nal is 3 hours, closed book; no notes, calculators, phones, etc. No clari cation will be given for any problems; if you believe a problem is ambiguous, interpret it as best you can and write down any assumptions you feel are necessary. Explain your answer (though you don"t have to prove that your answer is correct). is called the golden ratio. 2: use newton"s method to approximate the golden ratio. Start with one of the two integers you gave above, and iterate newton"s method two times (i. e. you should have your starting guess and then two re nements of this guess). Student #: a) prove that if x > 0, then, prove that. = lim h 0 log (cid:0)(1 + h/x)1/h(cid:1). (cid:0)1 + lim y (cid:1)y = e. Student #: let y(t) be the temperature of a body at time t. suppose that the body is in a water bath which remains at the constant temperature of 10 degrees.
