MATH 154 Study Guide - Fall 2018, Comprehensive Midterm Notes - Exponentiation, Tangent, Rational Function

• School: Simon Fraser University
• Department: Mathematics
• Course: MATH 154
• Professor: Yusuf Tuncer

Document Summary

The graphs of 2 functions intersect where the 2 functions are equal to each other. When we cancel x, we assume x 0, or treat x = 0 as a separate case. Between 0 & 1, values of x3 > values of x6, but x6 > x3 if x > 1. For large x-values, power functions with higher exponents dominate. For x-values close to 0, power functions with smaller exponents dominate. If we decrease the input of a power function (cid:4666)(cid:4667)= by dividing it by 10, output decreases. Limits are given by lim (cid:4666)(cid:4667)=; the limit of f(x), as x approaches a, equals l. If a function is undefined at a point but on both sides of that point values are getting close to a number, that number is the limit. May have left-hand & right-hand limits (as approaching a point from the left and right sides) by 10n. X a+ gives right-hand limit (approaching from right)