posted by cara on .
how would I do this limit?(by the way
-> is an arrow(
lim x-> 0 (5x^3+8x^2)/ (3x^4 - 16x^2)
When both the numerator and denominator evaluate to zero or infinity, the limit can be found by applying the d'hÃ´pital rule.
The rule states that if the limit of a division is indeterminate, the limit of the derivatives of the numerator and the denominator will equal the limit in question. The rule can be applied successively until either the denominator becomes defined and non-zero.
For the case in point,
denominator=f2(x)=(3x^4 - 16x^2)
Since f2(0)=0, we need to find the derivative
Again f21(0)=0, so we find the derivative
Now we have to evaluate
Therefore the limit x→0
(5x^3+8x^2)/ (3x^4 - 16x^2)