MATH 2554C Study Guide - Midterm Guide: Intermediate Value Theorem, Asymptote
13 Sep 2016
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Know the definitions of : lim x->a+ f(x)= l. Approach from the right side : lim x->a- f(x)= l. Approach from the left side": limits respect . When lim x->a f(x)= , - : horizontal asymptote. Techniques for evaluating limits: try to plug in the limit (* unless you try to divide by zero, try to rewrite the expression and then plug in. E. g. ) factoring & canceling: take limit as x approaching to +/- infinity of rational function. Look at leading terms: when top=bigger infinity, in case of x^3/ x^2 - infinity (negative value, when bottom is bigger 0, when leading terms are the same (e. g. ) mx^3/nx^3, the limit is m/n. Continuity: definition of f(x) is continuous . For any a in the domain of f, limit of f(x) x approaching to a is equals to f(a) You can evaluate limit of f(x) x approaching to a by plugging it in: most familiar functions= generally continuous at their domain.
