Let a function f: R → R be defined as f(x) = \ sin x - eˣ if x ≤ 0 a + [ - x] if 0 < x < 1 2x - b if x ≥ 1. where [ x ] is the greatest integer less than or equal to x. If f is continuous on R, then (a + b) is equal to:

Limit, Continuity and Differentiability: JEE Main 2021 Mathematics question

JEE Main 2021 · 20 Jul, Morning shift · Q4146

JEE Main 202120 Jul, Morning shiftMathematicsMediumLimit, Continuity and Differentiability420× since 2002

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:

JEE Main 2021 · 20 Jul, Morning shift · Q4146

JEE Main 202120 Jul, Morning shiftMathematicsMediumLimit, Continuity and Differentiability420× since 2002

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: