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\[\huge \lim_{x \rightarrow 5} \frac{ 1 }{ x-5 }\]

Does it exist?

yes

Are you sure about that?

not really

i completely forgot how to solve these except for direct substitution

okay thank you :)

how would i solve limits that have fractions over fraction though ?

Start by simplifying it into a single fraction.

\[\large \lim x \rightarrow -3 \frac{ \frac{ 1 }{ x } +\frac{ 1 }{ 3 }}{x+3}\]

ohh okay

(a/b)/c = a/(bc) and a/(b/c) = (ac)/b

Okay you need to add up the \(1/x\) and \(1/3\).

a/b + c/d = (ad + bc)/(bd)

\[\large \lim \rightarrow -3 \frac{ 3+x }{ 3x^2+9x }\]

This function becomes continuous once you have manipulated it a bit.

Continuous at \(-3\) at least.

what does that mean ?

ohh thankyou !