Question

Limit question! Will be posted below.

Answer 1

\[\lim_{x \rightarrow 0^+} 3\sqrt{x}lnx\]

Answer 2

have you tried writing it as a quotient
and see if l'hospital applies

Answer 3

I tried getting the derivative of it. But the answer key says the answer 0, and I'm not entirely sure why. @freckles

Answer 4

Getting the derivative and applying l'hospital's*

Answer 5

let's just ignore the 3 part for now

Answer 6

\[\lim_{x \rightarrow 0^+} \frac{\ln(x)}{\frac{1}{x^\frac{1}{2}}}\]

Answer 7

here we have -inf/inf
so we can use l'hospital

Answer 8

the derivative of ln(x) w.r.t. x is ?
the derivative of 1/(x^(1/2)) is w.r.t. x is?

Answer 9

1/x
and
-0.5sqrtx
?

Answer 10

\[\frac{d}{dx}(\frac{1}{x^{\frac{1}{2}}})=\frac{d}{dx}(x^{-\frac{1}{2}})=-\frac{1}{2}x^{\frac{-1}{2}-1}=\frac{-1}{2}x^{\frac{-3}{2}}=\frac{-1}{2 x^{\frac{3}{2}}}\]

Answer 11

\[l im_{x \rightarrow 0^+}\frac{\frac{1}{x}}{\frac{-1}{2 x^{\frac{3}{2}}}} \\ =\lim_{x \rightarrow 0^+} \frac{1}{x} \cdot \frac{2x^{\frac{3}{2}}}{-1} \]

Answer 12

Oh my god, careless mistakes. I get it now. Thank you! @freckles

Answer 13

np