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- For each function, decide whether it is continuous from the left at the given number, and whether it is continuous from the right.f(x) = \sqrt[4]{8 - 2x} at 4p(x) = \sqrt{x}\,\lfloor x \rfloor at 4r(x) = x^2 for x \ne 3, r(3) = 1, at 3
- Find the largest intervals on which each function is continuous.\sqrt{12 - 3x}\ln(x^2 - 4x)\sqrt{x + 3} - \dfrac{1}{x - 1}\dfrac{\sqrt{x}}{\ln x}
- Let $f
- Let $g
- Let k
- Let $s
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Continuity on an interval: the lesson ›More Chapter 1 worksheets: Limits and continuity
- 1.1What a limit is: graphs and tables
- 1.2One sided limits and when a limit exists
- 1.3The limit laws
- 1.4Limits by algebra: factoring and rationalizing
- 1.5The squeeze theorem and the limit of sine x over x
- 1.6Continuity at a point
- 1.7Continuity on an interval
- 1.8Infinite limits and vertical asymptotes
- 1.9Discontinuities and how to remove them
- 1.10Making a piecewise function continuous
- 1.11Limits at infinity and horizontal asymptotes
- 1.12Comparing growth rates at infinity
- 1.13The intermediate value theorem
- 1.14The epsilon delta definition of a limit