Question

What's L'Hopital's?

Please help me understand it.

Answer 1

what do you mean?

Answer 2

that's rule about limits, Izzy18970.

Answer 3

I haven't learned it & I'm in Calculus.

Answer 4

go here http://mathworld.wolfram.com/LHospitalsRule.html

Answer 5

it is that if:\[\lim_{x -> a} \frac{ f(x) }{ g(x) }= \frac{ 0 }{ 0 } or \frac{ \pm \infty }{ \pm \infty }\]then\[\lim_{x -> a} \frac{ f(x) }{ g(x) } = \lim_{x -> a} \frac{ f'(x) }{ g'(x) }\]

you take the derivative of the numerator and denominator separately (not to be confused with quotient rule) until 0/0 or infty/infty is no longer true

Answer 6

if we do it on:\[\lim_{x - >2} \frac{ x^3 - 4x }{ x^2 - 4 } = \frac{ 0 }{ 0 }\]\[\lim_{x - >2} \frac{ x^3 - 4x }{ x^2 - 4 } = \lim_{x - >2} \frac{ 3x^2 - 4}{ 2x } = \frac{ 3(2)^2 - 4 }{ 2(2) } = 2\]

Answer 7

if f(x) and g(x) have a limit and are differentiable, the limit of f(x)/g(x) is equal to the limit of f'(x)/g'(x).
there are a few more conditions. g(x) ≠ 0, f(x), g(x) both tend to +/- ∞ or both tend to 0.
this is the basic definition to understand the concept. it is not rigorous