Question

If `k != 0`, what is `\lim _ { x \rightarrow k } \frac { x ^ { 2} - k ^ { 2} } { x ^ { 2} - k x }`?

Answer 1

`2`

Explanation:

`lim_(x to k)(x^2-k^2)/(x^2-kx)`

By factoring out the numerator and the denominator,

`lim_(x to k)((x+k)cancel((x-k)))/(x cancel((x-k)))=(k+k)/k=(2 cancel(k))/(cancel k)=2`

I hope that this was clear.

Answer 2

`2`

Explanation:

`"factorise and simplify"`

`rArr(cancel((x-k))(x+k))/(xcancel((x-k)))=(x+k)/x`

`rArrlim_(xtok)(x^2-k^2)/(x^2-kx)`

`=lim_(xtok)(x+k)/x`

`=(2k)/k=2`