Define continuity of a function at a point x=a. Show that the function | Mathematics I 2077

Mathematics I20775 marksContinuity

Define continuity of a function at a point $x=a$ . Show that the function $f(x)=\sqrt{1-x^2}$ is continuous on the interval $[-1,1]$ . [5]

Define continuity of a function at a point $x=a$. Show that the function $f(x)=\sqrt{1-x^2}$ is continuous on the interval $[-1,1]$. [5]

--- A function f(x) is said to be continuous at a point x = a if the following three conditions are all satisfied: 1. f(a) is defined (the function has a value at x = a) 2. lim(x→a) f(x) exists (the left-hand limit equals the right-hand limit) 3. lim(x→a) f(x) = f(a) (the limit equals the functio...

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Define continuity of a function at a point x=a. Show that the function f(x)=sqrt1-x2 is continuous on the interval [-1,1].