# Math Help - One sided limits?

1. ## One sided limits?

Find the limit if it exists

1. As delta x approaches 0 limit from the left

((1/x+delta(x)-(1/x))/((delta(x))

2. This second limit is kind of confusing

As x approaches 3

where f(x)=

(x+2)/2 x < or equal to 3

12-2x/3 x>3

Would I just plug in 3+2/2=2.5?

2. ## Re: One sided limits?

Originally Posted by homeylova223
Find the limit if it exists
1. As delta x approaches 0 limit from the left
((1/x+delta(x)-(1/x))/((delta(x))
Is this the problem $\displaystyle\lim _{\delta x \to 0^ - } \dfrac{{\frac{1}{{x + \delta x}} - \frac{1}{x}}}{{\delta x}}~?$

3. ## Re: One sided limits?

Yes it is like that. I should learn that latex.

4. ## Re: One sided limits?

Determine for the fractions in the numerator a common denominator.

5. ## Re: One sided limits?

Originally Posted by homeylova223
Yes it is like that. I should learn that latex. PLEASE DO
$\frac{{\frac{1}{{x + \delta x}} - \frac{1}{x}}}{{\delta x}} = - \frac{{\delta x}}{{\delta x\left[ {x\left( {x + \delta x} \right)} \right]}}$

6. ## Re: One sided limits?

Originally Posted by homeylova223
Find the limit if it exists

1. As delta x approaches 0 limit from the left

((1/x+delta(x)-(1/x))/((delta(x))

[snip]
This has the form of a derivative from first principles, where f(x) = ...... and so the answer is f'(x) = ......

Originally Posted by homeylova223
Find the limit if it exists

[snip]

2. This second limit is kind of confusing

As x approaches 3

where f(x)=

(x+2)/2 x < or equal to 3

12-2x/3 x>3

Would I just plug in 3+2/2=2.5?
The right hand limit is 12 - 2(3)/3 = .... and the left hand limit is (3 + 2)/2 = ....

If right and left hand limits are the same then the limit exists and is equal to .... If right and left hand limits are not the same then the limit does not exist.