Calculus: lim x->0 (sin(x^8))/(x)
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Calculus: lim x->0 (sin(x^8))/(x)

[From: ] [author: ] [Date: 12-02-21] [Hit: ]
use radians for x, not degrees.......
Find the limit for the given function

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numerator and denominator evaluate to 0 so can use l'hopitals rule and differentiate top and bottom

lim x->0 8x^7 Cos[x^8]/ 1 = 0 *Cos[0] / 1 =0

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The limit is 0

This function does not satisfy l'Hopital's Rule as the numerator has no limit.

However, the denominator has a dampening effect of the the sine function. Making the multiplier of the sine smaller and smaller and eventually so close to 0 that it might as well be zero.

Please note, use radians for x, not degrees.

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using L'Hospitals rule

limx->0 (8x^7*cosx^8)/1

applying x=0

the limit comes to 0

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lim x->0 (sin(x^8))/(x)=lim x->0 [(sin(x^8))/x^8 * x^7]=0
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