Question

Limits and continuity. Please help.

Answer 1

To two decimal places, find the value of k that will make the function f(x) continuous everywhere.

Answer 2

\[f(x)=\left[\begin{matrix}3x+k, & x \le -4 \\ kx^2 -5, & x > -4\end{matrix}\right]\]

Answer 3

It's not a matrix, but a function with conditions I didn't know how to make that.

Answer 4

I know the basics of limits, but this one caught me off guard.

Answer 5

For the function to be continuous everywhere, it must be continuous at x=4. Therefore both conditions bust be equal at x=4 ie: \[3x+k=kx^{2}-5\] at x=4

From there plug in a known x and solve for k.

Answer 6

So, plug in x = 4? or something arbitrarily close to it?

Answer 7

Or rather, -4

Answer 8

I got -0.47 ish, and that's one of the answers. Thanks!