clara1223
  • clara1223
find the limit as h approaches 0 of h(3+(2/h^2))
Mathematics
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clara1223
  • clara1223
find the limit as h approaches 0 of h(3+(2/h^2))
Mathematics
schrodinger
  • schrodinger
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clara1223
  • clara1223
\[\lim_{h \rightarrow 0} h(3+\frac{ 2 }{ h ^{2} })\]
amistre64
  • amistre64
we can try some test points, say h=.0000001, and h=-.0000001 but what does your thoughts tell you initially?
clara1223
  • clara1223
Well I solved and got that the limit is 2, but that was wrong.

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amistre64
  • amistre64
your solution was flawed then :) we have 2 terms: ab if h < 0, a=-, b=+ ... ab = - if h > 0, a=+,b=+ ... ab=+
clara1223
  • clara1223
I don't understand.
amistre64
  • amistre64
let a=h let b=3+2/h^2 then multiply them together and yo have your setup. when h is less than zero, what are our signs for a and b? what about their product?
clara1223
  • clara1223
if h is less than 0 then a would be negative and b would be positive, and their products would both be negative
amistre64
  • amistre64
ok, so we have a left side limit that is negative ... now assume h is greater than zero ... what are the signs of a and b? and of their product?
clara1223
  • clara1223
if h is greater than 0 then a and b would both be positive and so would be their products.
clara1223
  • clara1223
oh, so since from the left it's negative and from the right it's positive, it doesnt exist?
amistre64
  • amistre64
so we have a right side limit that is positive can a positive limit ever be equal to a negative limit?
amistre64
  • amistre64
correct, its actually -inf and +inf so yeah
clara1223
  • clara1223
yeah, I graphed it and it helped me to understand.
amistre64
  • amistre64
graphs do help if applicable :)

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