Question

How do you find a value k such that the limit `xto1` exists given `(x^2-kx+9)/(x-1)`?

Answer 1

The limit of `x^2-kx+9`, as `xto1`, is finite and equals `-8`, for k = 10.

Explanation:

For a finite limit as `xto1`, `x-1` should be a factor of the

numerator.

The remainder upon division by `(x-1)` is `10-k = 0`. k = 10..

For this k, the ratio is `x-9 to -8` as `xto1`.