Question

lim as x approches y of [x-y]/[(y^2/x)-y]

Answer 1

\[\lim_{x \rightarrow y} (x-y)/{(y^2/x)-y}\] is this what you mean?

Answer 2

\[\lim_{x \rightarrow y} (x-y)\div[(y^2/x)-(y)]\]

Answer 3

this depends on what level of math you are in... because higher math can solve this, but beginning calculus would say that the limit does not exist because when you evaluate the problem, you get a 0 in the denominator

Answer 4

ok thank you :)

Answer 5

\[\lim_{x\rightarrow y}\frac{x-y}{y^2/x-y}=\lim_{x\rightarrow y}\frac{x(x-y)}{-y(x-y)}=-\lim_{x\rightarrow y}\frac{x}{y}=-1\quad(y\neq 0)\]

Answer 6

@nikvist. please explain how you got -y(x-y) in the denominator.

Answer 7

\[\frac{x-y}{y^2/x-y}\cdot\frac{x}{x}=\frac{x(x-y)}{-y(x-y)}\]