Find the value of k that makes f(x) continuous at x=-1 f(x)= ) -2x^2-2x&ifxleqslant -1 -kx+7&ifxgt -1 k= square

Question

Answer 1

To find the value of

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

, we need to ensure that the left-hand limit and the right-hand limit of \( f(x) \) at

are equal, and both equal to \( f(-1) \).First, let's find \( f(-1) \):

Next, we find the left-hand limit as

approaches -1:

Now, we find the right-hand limit as

approaches -1:

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

, these limits must be equal:

Solving for

:

Therefore, the value of

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

is:

Soru