How do I find the #lim_(x to 6) (5x)/(3+x^8)#?

Question

#lim_(x to 6) (5x)/(3+x^8)#

I'm confused, because the number it seems to approach is .00001786 when I plug 6 and numbers close to 6 inside. However, the website I have my math homework on says that it is incorrect. Undefined and 0 are also not accepted answers. Am I supposed to reduce this somehow? Or am I doing the order of operations wrong?

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Answer 1 · 2017-11-29T03:42:37

There is no discontinuity at the specified limit, therefore, the limit is is value at that point.

Given: #lim_(x to 6) (5x)/(3+x^8)#

The limit is merely the expression evaluate at the specified value:

#lim_(x to 6) (5x)/(3+x^8) = (5(6))/(3+(6)^8) = 10/559873#

This is a number very near 0 but it is not 0; it is not a surprise that the website says that 0 is an unacceptable answer.