Question

find the limit$\underset{x\to 1^{-}}{\lim }\sqrt{1-x^2}$

Short answer

$\underset{x\to 1^{-}}{\lim }\sqrt{1-x^2}=0$

Step-by-step solution

Step 1. Given information 

$\underset{x\to 1^{-}}{\lim }\sqrt{1-x^2}$

Step 2.  Limit of the function  

We can find limit of root function by $\underset{x\to c}{\lim }f\left(x\right)=f\left(c\right)$ if c is in the domain of f(x) and the domain of f(x)= $\sqrt{1-x^2}$is [-1,1]. So here c is -1 and it is in the domain. So we can use the above formula .

$$\begin{gathered} \underset{x\to 1}{\lim }f\left(x\right)=f\left(1\right) \\ =\sqrt{1-(1{)}^2}=0 \end{gathered}$$