Mathematics I207410 marksNumerical: piecewise function limitPrecise definition of Limit
A function is defined by Calculate f(-1), f(3), and sketch the graph. Prove that the limit does not exist. [5+0+5]
A function is defined by
$$f(x) = \begin{cases} x+2, & x<0 \ 1-x, & x>0 \end{cases}$$
Calculate $f(-1)$, $f(3)$, and sketch the graph. Prove that the limit does not exist.
$$\lim_{x \to 0} \frac{|x|}{x}$$
[5+0+5]
Given data: Piecewise function: $$f(x) = \begin{cases} x+2, & x<0 \ 1-x, & x0 \end{cases}$$ Note: $f(0)$ is undefined. Tasks: - Compute $f(-1)$ and $f(3)$, sketch graph [5 marks] - Prove $\displaystyle\lim{x\to 0}\frac{x}{x}$ does not exist [5 marks] All data present. --- f(-1): Since $-1 < 0$, ...