Evaluate lim \frac{3 {x}^(2) + 5x - 1 }{4 {x}^(3) + 2x + 6 } ​

Question

Evaluate lim

`\frac{3 {x}^(2) + 5x - 1 }{4 {x}^(3) + 2x + 6 }`
​

Answer 1

-1/6

Explanation:

To find the limit as x approaches 0 we can just plug in 0

for the numerator: 3*0+5*0-1 = -1

For the denominator: 4*0+2*0+6= 6

answer is just -1/6 or -.16666666666666666666667

Answer 2

`\lim_(x \to 0) =-(1)/(6)`

Explanation:

The first step in evaluating a limit should be to plug in the number to see if you get a result

When you plug in 0 to all of the x's in the expression, you are left with the constants -1 on the top and 6 on the bottom of the fraction.

So there's no need to go any further, the limit as x approaches 0 is
`-(1)/(6)`