Let f(x) is a function, defined as f(x)= begincases 3x2+2x+5;x0 4;x=0 x2-4x+3;x

Question

Let f(x) is a function, defined as f(x)= begincases 3x2+2x+5;x>0 4;x=0 x2-4x+3;x < 0 endcases then displaystyle lim x arrow 0+ f( x- sin x ) equals [ Note: ⋅ denotes fractional part function.] (A) 3 (B) 4 (C) 5 (D) None

Tardigrade Admin · Accepted Answer

If x=0+h ∴ .x-sinx. = .h-sinh. =(.h-sinh.)-[.h-sinh].=h-sinh ∴ f(.h-sinh.)=5

Q. Let $f (x)$ is a function, defined as $f (x) = ⎩ ⎨ ⎧ 3 x^{2} + 2 x + 5; x > 0 4; x = 0 x^{2} - 4 x + 3; x < 0$ then $x \to 0^{+} lim f ({x - sin x})$ equals $[$ Note: ${\cdot}$ denotes fractional part function.]

$3$

$4$

$5$

None

If $x = 0 + h$
$∴ {x - s in x} = {h - s inh}$
$= (h - s inh) - [h - s inh] = h - s inh$
$∴ f (h - s inh) = 5$

Q. Let f(x) is a function, defined as f(x)=⎩⎨⎧​3x2+2x+5;x>04;x=0x2−4x+3;x<0​ then x→0+lim​f({x−sinx}) equals [ Note: {⋅} denotes fractional part function.]

3

4

5

None

If x=0+h ∴{x−sinx}={h−sinh} =(h−sinh)−[h−sinh]=h−sinh ∴f(h−sinh)=5

Q. Let $f (x)$ is a function, defined as $f (x) = ⎩ ⎨ ⎧ 3 x^{2} + 2 x + 5; x > 0 4; x = 0 x^{2} - 4 x + 3; x < 0$ then $x \to 0^{+} lim f ({x - sin x})$ equals $[$ Note: ${\cdot}$ denotes fractional part function.]

$3$

$4$

$5$

If $x = 0 + h$
$∴ {x - s in x} = {h - s inh}$
$= (h - s inh) - [h - s inh] = h - s inh$
$∴ f (h - s inh) = 5$