Basic Mathematics2081.2Numerical: continuity and limitsContinuity definition
(question text pending review) # Solution ## Main Question [5 marks] Show that f(x) = 1 - sqrt1 - x2 is continuous on [-1,1] A function is continuous at a point c if $\lim_{x \to
(question text pending review) # Solution
Main Question [5 marks]
Show that $f(x) = 1 - \sqrt{1 - x^2}$ is continuous on $[-1,1]$
A function is continuous at a point $c$ if $\lim_{x \to
Definition: A function $f$ is continuous on a closed interval $[a,b]$ if it is continuous at every interior point and continuous from the right at $a$ and from the left at $b$. Given: $f(x) = 1 - \sqrt{1 - x^2}$, interval $[-1, 1]$. Step 1: Decompose into elementary functions $$f(x) = 1 - \sqrt{h...