# One sided limits?

• Jul 14th 2011, 01:53 PM
homeylova223
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?
• Jul 14th 2011, 02:13 PM
Plato
Re: One sided limits?
Quote:

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 $\displaystyle\lim _{\delta x \to 0^ - } \dfrac{{\frac{1}{{x + \delta x}} - \frac{1}{x}}}{{\delta x}}~?$

• Jul 14th 2011, 02:15 PM
homeylova223
Re: One sided limits?
Yes it is like that. I should learn that latex.
• Jul 14th 2011, 02:23 PM
Siron
Re: One sided limits?
Determine for the fractions in the numerator a common denominator.
• Jul 14th 2011, 02:23 PM
Plato
Re: One sided limits?
Quote:

Originally Posted by homeylova223
Yes it is like that. I should learn that latex. PLEASE DO

$\frac{{\frac{1}{{x + \delta x}} - \frac{1}{x}}}{{\delta x}} = - \frac{{\delta x}}{{\delta x\left[ {x\left( {x + \delta x} \right)} \right]}}$
• Jul 14th 2011, 09:11 PM
mr fantastic
Re: One sided limits?
Quote:

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) = ......

Quote:

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.