karabella98
  • karabella98
Find the limit as x approaches 0 from the left of [(1/(x+y))-(1/x)]/y
Calculus1
  • Stacey Warren - Expert brainly.com
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SOLVED
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chestercat
  • chestercat
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amistre64
  • amistre64
multiply top and bottom by x(x+y) to clear the fractions and simplify
beginnersmind
  • beginnersmind
Are you sure it's x->0+ not y->0+?
karabella98
  • karabella98
It's x -> 0-

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amistre64
  • amistre64
hmm, this might also seem to be f(x,y) stuff, multivariables
amistre64
  • amistre64
what does 'from the left' mean in multivariable ?
beginnersmind
  • beginnersmind
It means the same: x<0, I'm guessing.
amistre64
  • amistre64
i get a simplified form as: -y/[x(x+y)]
karabella98
  • karabella98
I know the right answer should be -1/x^2 but I can't get there
amistre64
  • amistre64
-1/(x(x+y)) but thats -1/x^2 only if y=0
amistre64
  • amistre64
are you sure your reading it correctly?
amistre64
  • amistre64
post a screen shot/pic if you can
karabella98
  • karabella98
I swear I'm blind it was y -> 0- you're right THANK YOU
amistre64
  • amistre64
yep
beginnersmind
  • beginnersmind
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
karabella98
  • karabella98
Thanks!!

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