Question

Find a reasonable estimate of the limit
Picture below

Answer 1

Hence, the limit of the function is:

1.5

Explanation:

We have to find a reasonable estimate of limit of the given expression:

`\lim_(x \to -1) (x^6-1)/(x^4-1)`

Since on putting the limit x=-1 we observe that the numerator and denominator both are equal to zero i.e we get a 0/0 form.Hence, we will apply L'hospitals rule to find the limit of the function.

We will firstly differentiate the numerator and denominator to obtain the limit.

On differentiating numerator we get:

`6x^5`

and on differentiating denominator we obtain:

`4x^3`

Hence, now we have to find the limit:

`\lim_(x \to -1) (6x^5)/(4x^3)\\\\=(6* (-1)^5)/(4* (-1)^3)\\\\=\frac{6* (-1)}[4* (-1)}\\\\=(-6)/(-4)\\\\=(6)/(4)\\\\=(3)/(2)\\\\=1.5`

Hence, the limit of the function is:

1.5