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15 Cards in this Set
- Front
- Back
- 3rd side (hint)
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if the limit from the left ≠ the limit on the right |
The limit DOES NOT EXIST |
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lim[c f(x)]= c [lim f(x)] |
Constant multiple |
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Lim [a f(x) ± b g(x)]= a lim f(x) ± b lim g(x) |
linear combination |
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Lim[f(x)g(x)]=[lim f(x)][lim g(x)] |
Product rule |
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Lim[f(x)/g(x)]=lim f(x)/ lim g(x) *provided g(x) ≠ 0 |
quotient rule |
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Lim [f(x)]^n=[lim f(x)]^n or lim[f(x)]^m/n =[lim f(x)]^m/n |
Power rule |
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Limit laws can be used to find the limits of polynomial, rational, and trigonometric functions by .... |
DIRECT SUBSTITUTION |
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When direct substitution produces the form 0/0, factor the numerator and denominator and cancel the common factors |
Cancellation technique |
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direct substitution produces 0/0, numerator & denominator NOT factorable, rationalize the numerator or denominator by the algebraic conjugate & cancel common factors |
Rationalization technique |
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Direct substitution produces 0/0 & the numerator & denominator has a compound rational expression, simplify by finding a common denominator & cancel the common factors |
Common denominator technique |
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Lim sin x/x = |
1 |
Special limit |
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Lim 1-cos x/x = |
0 |
Special limit |
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How is a vertical asymptote defined? |
If the lim as x approaches a from the left or the right is ± infinity |
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if n is an even integer then it will be a positive infinity |
Limits at infinity |
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If n is odd then it will be negative infinity |
Limits at infinity |
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