Question

My textbook gives the lim of (x^2-1)/x^4 as x approaches 0 to be neg infinity. I struggle to see how they got to neg infinity. Can anyone help me please?

Answer 1

when x-> 0
x^2 -1 tends to what ?

Answer 2

to - 1 ?

Answer 3

yes!
and denominator is 0
so what is -1/0 ?

Answer 4

denominator = 0 is undefined ?

Answer 5

ok, to check whether the limit is defined (or exists),
u check whether x->0+ f(x) and x->0- f(x) are equal

Answer 6

here they are equal, so this limit exist and has a value

Answer 7

to get that value , just put x=0 in f(x)

Answer 8

1/0 = infinity, -1/0 = - infinity

Answer 9

denominator is not zero, it is nearly zero.....means it has some teeny-weeny positive value and numerator is also not exactly -1 but some negative number
and so
quotient of a negative and positive numbers is negative

Answer 10

thanx a lot, i see now. much appreciated