Question

lim(x->0) [(1-2x^2)^1/5-(1+3x^2)^1/3]/x^2

Answer 1

or,
\[\Large \lim_{x \rightarrow 0}~ \left(\begin{matrix} \\ \frac{(1-2x^2)^{1/5}-(1+3x^2)^{1/3}}{x^2}\end{matrix}\right)\]

Answer 2

second

Answer 3

what can we solve without L'H'S?

Answer 4

there certainly are some things that we don't have to apply L'H"S to...

Answer 5

no, actually, nvm, just do L'H'S. I am sorry for confusing you.

\[\Large \lim_{x \rightarrow 0}~ \left(\begin{matrix} \\ \frac{(1-2x^2)^{1/5}-(1+3x^2)^{1/3}}{x^2}\end{matrix}\right)\]

Answer 6

it will involve a chain rule for each of the tops, for (1-2x^2)^1/5 and for the second one.

then we will need to simplify it.

can you first tell me what the derivative of (1-2x^2)^1/5) is ?

Answer 7

1/5*(1-2x^2)^-4/5*-4x