Use l'Hopital's rule to find the limit

Limx-infinity: xsin(10/x)

Please explain in full detail, I do not know the hopital rule that well.

Question

Use l'Hopital's rule to find the limit

Limx->infinity: xsin(10/x)

Please explain in full detail, I do not know the hopital rule that well.

anonymous · Answer

you can watch this video for help on hopital rule ( http://www.khanacademy.org/math/calculus/differential-calculus/v/introduction-to-l-hopital-s-rule)

tkhunny · Answer

Really big hint.

$x\cdot\sin\left(\dfrac{10}{x}\right) = \dfrac{\sin\left(\dfrac{10}{x}\right)}{\dfrac{1}{x}} = 10\cdot\dfrac{\sin\left(\dfrac{10}{x}\right)}{\left(\dfrac{10}{x}\right)}$

anonymous · Answer

just make x approach 0 instead, and change the function into sin(x/10)/x = 1/10

anonymous · Answer

$$xsin(10/x)$$

$$\sin \frac{ 10/x }{ x }$$

$$10\cos(10(0))$$

$$10$$

anonymous · Answer

is 10 the derivative...??

anonymous · Answer

which is the derivative??

anonymous · Answer

$$\frac{ d }{ dx } x \sin(\frac{ 10 }{ x }) = -\frac{ 10 } {x} \cos (\frac{ 10 }{ x })+\sin(\frac{ 10 }{ x })$$

anonymous · Answer

Thanks !!

anonymous · Answer

why is it positive 10 shouldn't it be -10

anonymous · Answer

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