MAT-100C Study Guide - Final Guide: Petri Dish, Hypotenuse, Trigonometry
25 Feb 2020
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Show that the domain and range of the function y = ln(1 ex+2) are ( , 2) and ( , 0) respectively. Using a theorem from class, show that the function f(x) = e x 2x3 + 1 has a root. Explain your reasoning and state the names of any theorems used. Simplify the expression 2 log4(2ex sin2 x) + log4(160. 5ex(1 sin2 x)) A certain type of bacteria in a petri dish triples every hour. For each of the following, evaluate the expression, or explain why it is unde ned. Suggestion: review the de nitions of sin 1 and cos 1. Solutions: domain: 1 ex+2 > 0 1 > ex+2 ( inf, 2) 0 > x + 2 2 > x, so domain is. Range: 1 ex+2 has domain ( , ), and range ( , 1, ln(1 ex+2) has domain ( , 2), and so we only take ln of (1 ex+2) for x values in ( , 2).
