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MATHEMATICS · Single correct · AP · Calculus AB · Limits and Continuity · Limits and Continuity

Problem

f(x) =

$b([x]^2 + [x]) + 1$	$\text{for } x \ge -1$
$\sin(\pi(x+a))$	$\text{for } x < -1$

, where

[x]

denotes the integral part of

x

, then for what values of

a, b

the function is continuous at

x = -1

? (1)

a = 2n + (3/2); b \in \mathbb{R}; n \in \mathbb{I}

(2)

a = 4n + 2; b \in \mathbb{R}; n \in \mathbb{I}

(3)

a = 4n + (3/2); b \in \mathbb{R}^+; n \in \mathbb{I}

(4)

a = 4n + 1; b \in \mathbb{R}^+; n \in \mathbb{I}