Let a function f : R $\to$ R be defined as $$f(x) = \left\{ {\matrix{
{\sin x - {e^x}} & {if} & {x \le 0} \cr
{a + [ - x]} & {if} & {0 < x < 1} \cr
{2x - b} & {if} & {x \ge 1} \cr
} } \right.$$
where [ x ] is the greatest integer less than or equal to x. If f is continuous on R, then (a + b) is equal to:
Solution
Continuous x = 0<br><br>f(0<sup>+</sup>) = f(0<sup>$-$</sup>) $\Rightarrow$ a $-$ 1 = 0 $-$ e<sup>0</sup><br><br>$\Rightarrow$ a = 0<br><br>Continuous at x = 1<br><br>f(1<sup>+</sup>) = f(1<sup>$-$</sup>)<br><br>$\Rightarrow$ 2(1) $-$ b = a + ($-$1)<br><br>$\Rightarrow$ b = 2 $-$ a + 1 $\Rightarrow$ b = 3<br><br>$\therefore$ a + b = 3
About this question
Subject: Mathematics · Chapter: Limits, Continuity and Differentiability · Topic: Limits and Standard Results
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