What rule is the Limit as x - 0 of x^n/kx^n= 1/k

Question

What rule is the Limit as x -> 0 of x^n/kx^n= 1/k

anonymous · Answer

It's been a while since limits and i'm doing multivariable calculus now and they are saying the x^n/x^n=1 if it goes to zero. I remember somewhat of that but I thought it was when it goes toward infinity

anonymous · Answer

just cancel out the x^n. you're left with 1/k

anonymous · Answer

ahh it's cancelled out gotcha the book doesn't explain that step so i was sitting here going, this still goes to zero

anonymous · Answer

not sure what they're going on about then... you're talking about $$\lim_{x \rightarrow 0}x^{n}/(k*x^{n})$$ right?

anonymous · Answer

after the x^n cancel out, if u use L'Hopital's rule to differentiate numerator and denominator both separately, you will get 0/1 which = 0.

why use L'Hopital's rule, because the value of k was unknown, and as x->0 the answer can't be left 1/k.