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burhan101
 2 years ago
Best ResponseYou've already chosen the best response.0\[\huge \lim_{x \rightarrow 5} \frac{ 1 }{ x5 }\]

burhan101
 2 years ago
Best ResponseYou've already chosen the best response.0i completely forgot how to solve these except for direct substitution

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

wio
 2 years ago
Best ResponseYou've already chosen the best response.3Make 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.

burhan101
 2 years ago
Best ResponseYou've already chosen the best response.0how would i solve limits that have fractions over fraction though ?

wio
 2 years ago
Best ResponseYou've already chosen the best response.3Start by simplifying it into a single fraction.

burhan101
 2 years ago
Best ResponseYou've already chosen the best response.0\[\large \lim x \rightarrow 3 \frac{ \frac{ 1 }{ x } +\frac{ 1 }{ 3 }}{x+3}\]

wio
 2 years ago
Best ResponseYou've already chosen the best response.3(a/b)/c = a/(bc) and a/(b/c) = (ac)/b

wio
 2 years ago
Best ResponseYou've already chosen the best response.3Okay you need to add up the \(1/x\) and \(1/3\).

burhan101
 2 years ago
Best ResponseYou've already chosen the best response.0\[\large \lim \rightarrow 3 \frac{ 3+x }{ 3x^2+9x }\]

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

wio
 2 years ago
Best ResponseYou've already chosen the best response.3This function becomes continuous once you have manipulated it a bit.

wio
 2 years ago
Best ResponseYou've already chosen the best response.3Continuous at \(3\) at least.

burhan101
 2 years ago
Best ResponseYou've already chosen the best response.0what does that mean ?

wio
 2 years ago
Best ResponseYou've already chosen the best response.3What 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.

Kainui
 2 years ago
Best ResponseYou've already chosen the best response.0Ask 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.
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