Question

Find the limit as x approaches 0 from the left of [(1/(x+y))-(1/x)]/y

Answer 1

multiply top and bottom by x(x+y) to clear the fractions and simplify

Answer 2

Are you sure it's x->0+ not y->0+?

Answer 3

It's x -> 0-

Answer 4

hmm, this might also seem to be f(x,y) stuff, multivariables

Answer 5

what does 'from the left' mean in multivariable ?

Answer 6

It means the same: x<0, I'm guessing.

Answer 7

i get a simplified form as:

-y/[x(x+y)]

Answer 8

I know the right answer should be -1/x^2 but I can't get there

Answer 9

-1/(x(x+y))

but thats -1/x^2 only if y=0

Answer 10

are you sure your reading it correctly?

Answer 11

post a screen shot/pic if you can

Answer 12

I swear I'm blind it was y -> 0- you're right THANK YOU

Answer 13

yep

Answer 14

If you have problems with the algebra, read this pdf:
It uses x_0 for x and deltax for y, but otherwise it's the same limit.

http://ocw.mit.edu/courses/mathematics/18-01sc-single-variable-calculus-fall-2010/1.-differentiation/part-a-definition-and-basic-rules/session-2-examples-of-derivatives/MIT18_01SCF10_Ses2a.pdf

Answer 15

Thanks!!