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Worksheets›Calculus›Limits

Calculus Limits Worksheets

Limits by direct substitution, limits of 0/0 forms by factoring and rationalizing, limits at infinity, and one-sided limits and continuity from graphs. Every sheet comes with a computed answer key.

Make a mixed limits sheet
Limits by direct substitutionlimx→4 −3x + 6x + 9Evaluate limits of polynomial and rational functions at points where they are continuous by substituting the value.Limits by factoring (0/0 forms)limx→6 3x2 − 14x − 24x2 − 3x − 18Evaluate limits that give 0/0 on substitution by factoring and cancelling the common factor, or by rationalizing.Limits at infinitylimx→∞ −7x3 − 2x2 − 2x + 53x3 + x2 + x − 3Find limits of rational functions as x grows without bound by comparing the degrees of the top and bottom.One-sided limits and continuitylimx→−3 f(x)xy−6−4−20246−6−4−20246Read one-sided limits, two-sided limits and function values from a graph, and decide whether the function is continuous or has a jump or removable discontinuity.