Calculate  $\lim\limits_{ x\rightarrow 100 }{ \frac { 10-\sqrt { x } }{ x+5 } }$ $$\lim_{ x\rightarrow 100 }{ \frac { 10-\sqrt { x }  }{ x+5 }  } $$
Could you explain how to do this without using a calculator and using basic rules of finding limits?
Thanks

Recall that $\lim_{x \to a} f(x) = f(a)$ if $f(x)$ is continuous at $a$. The function $f(x) = \dfrac{10-\sqrt{x}}{x+5}$ is continuous at $100$ since the numerator $10-\sqrt{x}$ is continuous for all $x > 0$ and the denominator $5+x$ is continuous for all $x$. Hence, the function $f(x) = \dfrac{10-\sqrt{x}}{x+5}$ is continuous for all $x > 0$. Now you should be able to finish it off.
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Hence, $$\lim_{x \to 100} \dfrac{10-\sqrt{x}}{x+5} = \dfrac{10 - \sqrt{100}}{100 + 5} = \dfrac{10 - 10}{105} = 0$$

