How do you find the derivative of # y=sqrt(x−3)# using the limit definition?
1 Answer
Given:
Then:
Using the limit definition:
Substitute in the functions:
We know that, if we multiply the numerator by
Please observe that we have not changed the value of anything, because we have multiplied by 1 in a very special form.
Now, the radicals in the numerator disappear, because of the property
Combine like terms in the numerator:
The h in the numerator cancels with the h in the denominator:
Now we can allow h to become 0:
Combine like terms: