Printable View
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?
Is this the problem $\displaystyle \displaystyle\lim _{\delta x \to 0^ - } \dfrac{{\frac{1}{{x + \delta x}} - \frac{1}{x}}}{{\delta x}}~?$Quote:
Originally Posted by homeylova223
Please learn to post readable questions.
Yes it is like that. I should learn that latex.
Determine for the fractions in the numerator a common denominator.
$\displaystyle \frac{{\frac{1}{{x + \delta x}} - \frac{1}{x}}}{{\delta x}} = - \frac{{\delta x}}{{\delta x\left[ {x\left( {x + \delta x} \right)} \right]}}$Quote:
Originally Posted by homeylova223
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
The right hand limit is 12 - 2(3)/3 = .... and the left hand limit is (3 + 2)/2 = ....Quote:
Originally Posted by homeylova223
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.
