wodb #2 Calculus

Susan Robinson
Flashcards by Susan Robinson, updated more than 1 year ago
Susan Robinson
Created by Susan Robinson about 5 years ago


Introduction to Continuity

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Question Answer
other functions are likely rational functions only continuous function limit as x approaches -2 is equal to the function value no asymptotes, points of discontinuities or jumps
has a limit where there is no funciton value limit as x approaches -2 is -4 there is no function value at x=-2
no x-interceps, different y-intercept only graph with curves only one with an asymptote limit as x approaches -2 does not exist
the only piecewise function as x approaches -2, the limit is -4 but the function value at x=-2 is -3
What are the conditions of point continuity? At x=a, f(x) is continuous if: 1. limit as x approaches a exists 2. the function value at x=a exists 3. the limit and the function value are the same
Different kinds of discontinuity removeable discontinuity: there is a hole that can be filled up infinite discontinuity: there is a vertical asymptote jump discontinuity: the function jumps from one value to another at a point
Continuous Functions polynomial functions exponential functions sinusoidal functions-sine and cosine absolute value functions log functions & radical functions are continous on their domain
Functions with continuity issues piecewise function: you need to check what's happening at the points where the pieces change rational functions: you need to check for vertical aymptotes and holes
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