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
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.
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
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