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burhan101Best ResponseYou've already chosen the best response.0
\[\huge \lim_{x \rightarrow 5} \frac{ 1 }{ x5 }\]
 one year ago

burhan101Best ResponseYou've already chosen the best response.0
i completely forgot how to solve these except for direct substitution
 one year ago

wioBest ResponseYou've already chosen the best response.3
Well, when you can't directly substitute, I recommend putting in really close values (e.g. 5.001 and 4.999).
 one year ago

wioBest ResponseYou've already chosen the best response.3
Make sure it exists first. Then you can use things like squeeze theorem / l'Hospital's rule. There is no sure way of doing limits, only a series of methods.
 one year ago

burhan101Best ResponseYou've already chosen the best response.0
how would i solve limits that have fractions over fraction though ?
 one year ago

wioBest ResponseYou've already chosen the best response.3
Start by simplifying it into a single fraction.
 one year ago

burhan101Best ResponseYou've already chosen the best response.0
\[\large \lim x \rightarrow 3 \frac{ \frac{ 1 }{ x } +\frac{ 1 }{ 3 }}{x+3}\]
 one year ago

wioBest ResponseYou've already chosen the best response.3
(a/b)/c = a/(bc) and a/(b/c) = (ac)/b
 one year ago

wioBest ResponseYou've already chosen the best response.3
Okay you need to add up the \(1/x\) and \(1/3\).
 one year ago

wioBest ResponseYou've already chosen the best response.3
a/b + c/d = (ad + bc)/(bd)
 one year ago

burhan101Best ResponseYou've already chosen the best response.0
\[\large \lim \rightarrow 3 \frac{ 3+x }{ 3x^2+9x }\]
 one year ago

wioBest ResponseYou've already chosen the best response.3
I don't think you're doing it correctly. \[ \frac{1}{x} +\frac{1}{3} = \frac{x+3}{3x} \]And then \[\Large \frac{\frac{x+3}{3x}}{x+3} = \frac{x+3}{3x(x+3)} = \frac{1}{3x} \]
 one year ago

wioBest ResponseYou've already chosen the best response.3
This function becomes continuous once you have manipulated it a bit.
 one year ago

wioBest ResponseYou've already chosen the best response.3
Continuous at \(3\) at least.
 one year ago

burhan101Best ResponseYou've already chosen the best response.0
what does that mean ?
 one year ago

wioBest ResponseYou've already chosen the best response.3
What does continuous mean? It means: 1) \(f(a)\) is defined 2) \(\lim_{x \to a}f(x)\) exists and 3) \(\lim_{x \to a}f(x) = f(a) \) In general, it means you can just plug \(a\) into \(f(x)\) and get the answer to the limit.
 one year ago

KainuiBest ResponseYou've already chosen the best response.0
Ask yourself, what is a limit? Really. It's what happens as you approach a number from both sides. So to approach a number, you can plug in numbers close to it, like 4.999 is close to 5 on the left side while 5.00001 is close on the right side. Make sense? Plugging these in and seeing what you approach is really the essence of a limit and understanding that will let you solve any limit problem by simply graphing it when you get stumped.
 one year ago
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