Question

Find the limit of each function;
a) as x approaches infinity
b) as x approaches negative infinity
f(x)=(2/x)-3

Answer 1

both a and b = -3

Answer 2

@Hoa I am confused how both equals -3?

Answer 3

is that \[(2/x) - 3\]

or is that "-3" an exponent?

Answer 4

I'll assume it is the first one.....(2/x) - 3

now ask yourself....what happens as x gets infinitely big?

well since its in the denominator....the number gets closer and closer to 0 right?

think about 1/10....thats .10....now 1/100...thats .01....1/1000....that .01 ...closer and closer to 0 right?

so if 2/x...gets closer and closer to zero.....and the 3 is subtracted from it......that would approach -3 right?

now with - infinity....the same thing......we still approach 0...just from a different side......then still subtract 3....so we still approach -3

Answer 5

lim 2/x \[\lim_{x \rightarrow \infty}(\frac{ 2 }{ x } -3 ) = \lim_{x \rightarrow \infty}\frac{ 2 }{ x } -\lim_{x \rightarrow \infty}3\]= 0 -3 = -3

Answer 6

the same thing with - infinitive.

Answer 7

is it your problem or else? (2/x) -3 or (2/x)^-3? if it's latter, the things is different.

Answer 8

if yours is \[(\frac{ 2 }{ x })^-3\] then the answer is infinitive or - infinitive respectively

Answer 9

do you know why? because (2/x)^-3 = x^3 /2. x--> infinitive , limit of x is approaches infinitive, too.

Answer 10

sorry, x^3/8

Answer 11

@johnweldon1993 its like this in the input

Answer 12

yeah exactly...that's what I assumed....then my explanation stands :)