If f(x)=| sin x cos x tan x x3 x2 x 2 x 1 1| then undersetx arrow 0Lt (f(x)/x2) is

Question

If f(x)=| sin x cos x tan x x3 x2 x 2 x 1 1| then undersetx arrow 0Lt (f(x)/x2) is (A) -1 (B) 3 (C) 1 (D) 0

Tardigrade Admin · Accepted Answer

f(x)= sin x(x2-x)- cos x(x3-2 x2)+ tan x(x3-2 x3) undersetx arrow 0 lt(f(x)/x2)= undersetx arrow 0lt( sin x-( sin x/x)-(x-2) cos x-x tan x) =0-1-(0-2) x 1-0=-1+2=1

Q. If $f (x) = ∣ ∣ sin x x^{3} 2 x cos x x^{2} 1 tan x x 1 ∣ ∣$ then $_{x \to 0} L t \frac{f ( x )}{x ^{2}}$ is

-1

3

1

0

$f (x) = sin x (x^{2} - x) - cos x (x^{3} - 2 x^{2}) + tan x (x^{3} - 2 x^{3})$
$_{x \to 0} lt \frac{f ( x )}{x ^{2}} =_{x \to 0} lt (sin x - \frac{s i n x}{x} - (x - 2) cos x - x tan x)$
$= 0 - 1 - (0 - 2) x 1 - 0 = - 1 + 2 = 1$

Q. If f(x)=∣∣​sinxx32x​cosxx21​tanxx1​∣∣​ then x→0​Lt​x2f(x)​ is

-1

3

1

0

f(x)=sinx(x2−x)−cosx(x3−2x2)+tanx(x3−2x3) x→0​lt​x2f(x)​=x→0​lt​(sinx−xsinx​−(x−2)cosx−xtanx) =0−1−(0−2)x1−0=−1+2=1

Q. If $f (x) = ∣ ∣ sin x x^{3} 2 x cos x x^{2} 1 tan x x 1 ∣ ∣$ then $_{x \to 0} L t \frac{f ( x )}{x ^{2}}$ is

$f (x) = sin x (x^{2} - x) - cos x (x^{3} - 2 x^{2}) + tan x (x^{3} - 2 x^{3})$
$_{x \to 0} lt \frac{f ( x )}{x ^{2}} =_{x \to 0} lt (sin x - \frac{s i n x}{x} - (x - 2) cos x - x tan x)$
$= 0 - 1 - (0 - 2) x 1 - 0 = - 1 + 2 = 1$