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use continuity to evaluate the limit
- Thread starter smp
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HallsofIvy
Elite Member
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- Jan 27, 2012
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Since sine is a continuous function, that is \(\displaystyle 5 sin(\pi+ sin(\pi))\)
Since sine is a continuous function, that is \(\displaystyle 5 sin(\pi+ sin(\pi))\)
Or, just to be silly, \(\displaystyle 5 sin(\pi+ sin(\pi + sin(\pi + sin(\pi))))\)
HallsofIvy
Elite Member
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- Jan 27, 2012
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- 7,760
Trouble maker!
smp, you titled this "use continuity to evaluate the limit". If you are given such a problem, surely you must know what continuous means!
"A function, f, is "continuous" at x= a if and only if
1) f(a) exists
2) \(\displaystyle \lim_{x\to a} f(x)\) exists
3) \(\displaystyle \lim_{x\to a}f(x)= f(a)\)
So by definition, the limit of a continuous function is just its value at that point.
smp, you titled this "use continuity to evaluate the limit". If you are given such a problem, surely you must know what continuous means!
"A function, f, is "continuous" at x= a if and only if
1) f(a) exists
2) \(\displaystyle \lim_{x\to a} f(x)\) exists
3) \(\displaystyle \lim_{x\to a}f(x)= f(a)\)
So by definition, the limit of a continuous function is just its value at that point.