Evaluate the limit lim x → 4^- (x-5)/4-x

Good question! You are right! If we substitute the value of x = 4 in the expression we'll get infinity. Now we should find if it is negative or positive

The value of x approaches 4^- which means x approaches the 4 from the left side.

So we could assume it would be 3.99, 3.999, 3.999, ...

If we substitute them in our question, we'll get -ve in the numerator and +ve denominator. -ve over +ve is -ve. So the answer is -ve infinity.

= $\lim_{x \to 4^-} \frac{(x-5) \, \rarr \, -ve}{(x-4) \, \rarr \, +ve}$

= -∞