as x-> + infinity (limit)
3x^4-2x^2/x^4+5x^2
i got positive infinity. is this right
multiply numerator by 1/x^4
(3-2/x^2) / (1+5/x^2) so the limit is 3
i don't get why you would multiply the numerator by that. please explain
To find the limit as x approaches positive infinity for the given expression (3x^4-2x^2)/(x^4+5x^2), you need to evaluate the expression at x = + infinity.
First, we look at the highest power of x in the numerator and denominator. In this case, both the numerator and denominator have a leading term of x^4.
Since x is approaching positive infinity, the highest power term of x (x^4) will dominate the expression.
Now, divide both the numerator and denominator by x^4 to simplify the expression:
(3x^4/x^4 - 2x^2/x^4) / (x^4/x^4 + 5x^2/x^4)
Simplifying further:
(3 - 2/x^2) / (1 + 5/x^2)
Now, as x approaches positive infinity, 2/x^2 and 5/x^2 will tend to zero since x^2 becomes infinitely large. Therefore, we can ignore these terms.
The simplified expression becomes:
(3 - 0) / (1 + 0)
Which equals 3/1, which is equal to 3.
Therefore, the limit of the given expression as x approaches positive infinity is 3.