Question

Evaluate the limit of

Answer 1

Option a is correct --
`(9)/(2)`

Explanation:

If we put infinity directly into the expression we get ∞ + ∞ expression. In order to circumvent it we divide both numerator and denominator with the greatest exponent.

`\lim_(x \to \infty) (9n^(3)+5n-2)/(2n^(3))`

Divide each term by n³

`=\lim_(x \to \infty) ((9n^(3))/(n^(3))+(5n)/(n^(3)) -(2)/(n^(3)))/((2n^(3))/(n^(3)) )`

`=\lim_(x \to \infty)(9(1)+(5)/(n^(2))-(2)/(n^(3)))/(2(1)) } \\=\lim_(x \to \infty)(9+(5)/(n^(2))-(2)/(n^(3)))/(2)} \\\\by putting n = infinity (5)/(n^(2)) becomes 0 and(2)/(n^(3)) becomes 0 \\=(9+0-0)/(2) \\=(9)/(2)`