Find the value of k that makes f(x) continuous at x=-1 f(x)= ) (2x^3+2x^2)/(x+1)&ifxneq -1 k&ifx=-1 k= square

Question

Answer 1

To find the value of

that makes \( f(x) \) continuous at

, we need to ensure that the limit of \( f(x) \) as

approaches

is equal to \( f(-1) \).First, let's find the limit of \( f(x) \) as

approaches

. We start by simplifying the expression for \( f(x) \) when

:

We can factor the numerator:

For

, we can cancel out the

terms:

Now, we take the limit of this simplified expression as

approaches

:

For \( f(x) \) to be continuous at

, we need:

Thus, we set

equal to the limit we found:

Therefore, the value of

that makes \( f(x) \) continuous at

is:

Soru