Question

`\lim_(n \to \infty) a_n`
`(x)/(y)`2x³+2×-ײ
÷ײ·

Answer 1

The calculated limit
`\lim_(x \to \infty) a_x` of the expression
`a(x) = (2x\³ + 2x - x^2)/(x^2)` is ∝

How to evaluate the limit expression

From the question, we have the following parameters that can be used in our computation:

`a(x) = (2x\³ + 2x - x^2)/(x^2)`

Also, we have the limits to be

`\lim_(x \to \infty) a_x`

So, we have

`\lim_(x \to \infty) a_x = \lim_(x \to \infty) ((2x\³ + 2x - x^2)/(x^2))`

Evaluate the quotient

So, we have

`\lim_(x \to \infty) a_x = \lim_(x \to \infty) (2x + (2)/(x) - 1)`

Substitute the known values into the equation

`\lim_(x \to \infty) a_x = (2 * \infty + (2)/(\infty) - 1)`

This gives

`\lim_(x \to \infty) a_x = \infty + 0 - 1`

Evaluate

`\lim_(x \to \infty) a_x = \infty`

Hence, the limit of the expression is ∝

Question

Determine the following limits

`\lim_(x \to \infty) a_x`

`a(x) = (2x\³ + 2x - x^2)/(x^2)`