Daily Math · 2026-06-02

Question 1

For $f(x) = \begin{cases} x + 1, & x < 0 \ x^2 + 1, & x \ge 0 \end{cases}$, $f$ is continuous at $x = 0$ because:

Accepted Answer

$\lim_{x 	o 0^-}f = \lim_{x 	o 0^+}f = f(0) = 1$

Answer

$f(0)$ is undefined

Answer

The left and right limits differ

Answer

$f$ is a polynomial

Question 2

The solution set of $|x - 2| < 3$ is:

Accepted Answer

$(-1, 5)$

Answer

$(-3, 3)$

Answer

$(2, 5)$

Answer

$[-1, 5]$

Question 3

Evaluate $\displaystyle\lim_{x	o 0} \dfrac{1 - \cos(x)}{x^2}$.

Accepted Answer

$\dfrac{1}{2}$

Answer

$0$

Answer

$\dfrac{1}{4}$

Answer

$1$