Question

simple limit but i am blank

Answer 1

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

Answer 2

Does it exist?

Answer 3

yes

Answer 4

Are you sure about that?

Answer 5

not really

Answer 6

i completely forgot how to solve these except for direct substitution

Answer 7

Well, when you can't directly substitute, I recommend putting in really close values (e.g. 5.001 and 4.999).

Answer 8

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.

Answer 9

okay thank you :)

Answer 10

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

Answer 11

Start by simplifying it into a single fraction.

Answer 12

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

Answer 13

ohh okay

Answer 14

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

Answer 15

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

Answer 16

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

Answer 17

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

Answer 18

I don't think you're doing it correctly. \[
\frac{1}{x} +\frac{1}{3} = \frac{x+3}{3x}
\]And then \[\Large
\frac{\frac{x+3}{3x}}{x+3} = \frac{x+3}{3x(x+3)} = \frac{1}{3x}
\]

Answer 19

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

Answer 20

Continuous at \(-3\) at least.

Answer 21

what does that mean ?

Answer 22

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.

Answer 23

ohh thankyou !

Answer 24

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.