Question

Find the limit of the function algebraically.
lim x->0 (x^2+2x)/(x^4)

Answer 1

factor out x from the numerator,
what u get ?

Answer 2

x(x+2)/x^4
???

Answer 3

yes,
anything getting cancelled ?
simplify that...

Answer 4

x+2/x^3

Answer 5

correct, since you cancelled the factor, that made the numerator = 0
now if you plug in x=0 , numerator is not longer = 0

so just plug in x=0 , what do u get ?

Answer 6

Error?

Answer 7

Error is because there is a 0 in the denominator, and mathematically that is illegal!

Answer 8

lol, no error, our calculators cannot calculate that

anything positive / 0 = \(+\infty \)
anything negative / 0 = \(-\infty \)

so our numerator is positive or negative ?

Answer 9

- infinity

Answer 10

numerator is negative ? how ?

Answer 11

2/0?

Answer 12

numerator = x+2

since \(x\to 0\), x is very near to 0
so, x+2 will be positive!
makes sense ?

Answer 13

\(+2/0 =+\infty \)

Answer 14

do you have choices/options for this question ?

Answer 15

lim x->0 (x^2+2x)/(x^4)
= x(x+2)/x^4
= x+2/x^3
= lim x-> 0 - (x+2) = 2
= lim x-> 0 - (x^3) = 0
= 2/0
= + infinity

Answer 16

that would be correct

Answer 17

Thank you very much!

Answer 18

though more appropriate step would be

lim x-> 0 (x+2)/x^3 = (0+2)/0 = +infinity

don't break limit into numerator and denominator

Answer 19

lim x->0 (x^2+2x)/(x^4)
= x(x+2)/x^4
= x+2/x^3
= lim x-> 0 (x+2)/x^3 = (0+2)/0 = +infinity