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Calculus question (Surprisingly, I'm not asking for homework answers)?
When finding the slope of a tangent line where the function is something like 1/x, my calculus book has a proof, and I don't understand how to go from one step to the other.
limit as h->0 ((1/a+h)-(1/a))/h
= limit as h->0 (1/h) * (a-(a+h))/a(a+h)
Care to explain?
1 Answer
- Math WizLv 61 decade agoFavorite Answer
((1/(a + h)) - (1/a)) / h
Instead of dividing everything by h, multiply everything by 1/h:
= (1/h) * ((1/(a + h)) - (1/a))
Get a common denominator: a * (a + h)
= (1/h) * (((1 * a)/(a * (a + h))) - ((1 * (a + h))/(a * (a + h)))
Combine the fractions:
= (1/h) * (((1 * a) - ((1 * (a + h))) / (a * (a + h))
Simply the numerator:
= (1/h) * (a - (a + h)) / (a * (a + h))