# Multi-Variable Limit Problem

• Aug 27th 2011, 12:04 PM
Lane61190
Multi-Variable Limit Problem
Question...

ƒ(x,y) = (4x²) / (1x²+5y²)
lim (x,y)→(0,0)

What is the limit along the line y=mx

My Attempt
The function then becomes...

ƒ(x,mx) = (4x²) / (1x²+5mx²)
lim (x,mx)→(0,0)

I thought the answer was then as easy as dropping all the variables and seeing that approaching the origin the function is closest to 4/6, but this is incorrect.

What am I not understanding?
• Aug 27th 2011, 01:59 PM
TheChaz
Re: Multi-Variable Limit Problem
First, don't forget that:
\$\displaystyle (mx)^2 = m^2x^2 \$

Why would you "drop" the variables? You have (4x²) / (1x²+5m²x²) = (4x²) / [(1+5m²)x²] = 4/(1 + 5m²)
• Aug 27th 2011, 02:20 PM
Lane61190
Re: Multi-Variable Limit Problem
Quote:

Originally Posted by TheChaz
First, don't forget that:
\$\displaystyle (mx)^2 = m^2x^2 \$

Don't I feel stupid! Totally forgot my parenthesis. I had tried the answer 4/(1+5m) and when it wasn't correct I assumed the problem was more than a silly distribution error. Thanks for the help, that's what I was looking for!
• Aug 27th 2011, 02:48 PM
TheChaz
Re: Multi-Variable Limit Problem
No problemo.