Question

[3 -sqrt(5+x)] / (x-4). find limit as x reaches 4.

Answer 1

the answer is -1/6, but i don't know how!

Answer 2

There's the trial option, where you pick values of x that are close to 4, and see what number comes out.

For example,
x=3: f(x) = 0.172
x=5: f(x) = 0.162
x=3.9999: f(x) = 0.16667
x=4.0001: f(x) = 0.16667

Answer 3

Oh also, L'hopital's Rule can be used, if you're studying calculus
\[\lim_{x \rightarrow 4} \frac{f(x)}{g(x)} = \lim_{x \rightarrow 4} \frac{f'(x)}{g'(x)}\]

Answer 4

If\[f(x) = 3 - \sqrt{5+x} \text{ then } f'(x) = \frac{1}{2\sqrt{5+x}}\]If\[g(x)=x-4 \text{ then } g'(x) = 1\]

Answer 5

Sorry, f'(x) is negative.

Answer 6

thanks