Question

find the limit as h approaches 0 of h(3+(2/h^2))

Answer 1

\[\lim_{h \rightarrow 0} h(3+\frac{ 2 }{ h ^{2} })\]

Answer 2

we can try some test points, say h=.0000001, and h=-.0000001

but what does your thoughts tell you initially?

Answer 3

Well I solved and got that the limit is 2, but that was wrong.

Answer 4

your solution was flawed then :)

we have 2 terms: ab

if h < 0, a=-, b=+ ... ab = -
if h > 0, a=+,b=+ ... ab=+

Answer 5

I don't understand.

Answer 6

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?

Answer 7

if h is less than 0 then a would be negative and b would be positive, and their products would both be negative

Answer 8

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?

Answer 9

if h is greater than 0 then a and b would both be positive and so would be their products.

Answer 10

oh, so since from the left it's negative and from the right it's positive, it doesnt exist?

Answer 11

so we have a right side limit that is positive

can a positive limit ever be equal to a negative limit?

Answer 12

correct, its actually -inf and +inf so yeah

Answer 13

yeah, I graphed it and it helped me to understand.

Answer 14

graphs do help if applicable :)