Mathematics I207510 marksNumerical: piecewise function limitPrecise definition of Limit
A function is defined by f(x) = |x| Calculate f(-3), f(4), and sketch the graph. Prove that the limit does not exist. [5+0+5]
A function is defined by $f(x) = |x|$
Calculate $f(-3)$, $f(4)$, and sketch the graph.
Prove that the limit does not exist. $$\lim_{x \to 2} \frac{|x-2|}{x-2}$$ [5+0+5]
- Function: $f(x) = x$ - Required: $f(-3)$, $f(4)$, sketch of $y = x$ - Limit to analyze: $\displaystyle\lim{x \to 2} \frac{x-2}{x-2}$ - Marks split: [5 + 0 + 5] --- The absolute value function is defined piecewise as: $$f(x) = x = \begin{cases} x & \text{if } x \geq 0 \ -x & \text{if } x < 0 \e...