The value of displaystyle lim x arrow-∞ (x2 tan (1/x)/√4 x2-x+1) is equal to

Question

The value of displaystyle lim x arrow-∞ (x2 tan (1/x)/√4 x2-x+1) is equal to (A) 1 (B) (1/2) (C) -1 (D) -(1/2)

Tardigrade Admin · Accepted Answer

Let L= displaystyle lim x arrow-∞ (x2 tan (1/x)/√4 x2-x+1) Taking out x from square root in denominator, we get L = displaystyle lim x arrow-∞ (x ( tan (1/x)/(1)x)/-x √4-(1)x+(1)x2 =(1/-√4) =-(1/2)

Q. The value of $x \to - \infty lim \frac{x ^{2} tan \frac{1}{x}}{4 x ^{2} - x + 1}$ is equal to

$1$

$\frac{1}{2}$

$- 1$

$- \frac{1}{2}$

Let $L = x \to - \infty lim \frac{x ^{2} tan \frac{1}{x}}{4 x ^{2} - x + 1}$
Taking out $x$ from square root in denominator, we get
$L = x \to - \infty lim \frac{x \frac{t a n \frac{1}{x}}{\frac{1}{x}}}{- x 4 - \frac{1}{x} + \frac{1}{x ^{2}}}$
$= \frac{1}{- 4}$
$= - \frac{1}{2}$

Q. The value of x→−∞lim​4x2−x+1​x2tanx1​​ is equal to

1

21​

−1

−21​

Let L=x→−∞lim​4x2−x+1​x2tanx1​​ Taking out x from square root in denominator, we get L=x→−∞lim​−x4−x1​+x21​​xx1​tanx1​​​ =−4​1​ =−21​

Q. The value of $x \to - \infty lim \frac{x ^{2} tan \frac{1}{x}}{4 x ^{2} - x + 1}$ is equal to

$1$

$\frac{1}{2}$

$- 1$

$- \frac{1}{2}$

Let $L = x \to - \infty lim \frac{x ^{2} tan \frac{1}{x}}{4 x ^{2} - x + 1}$
Taking out $x$ from square root in denominator, we get
$L = x \to - \infty lim \frac{x \frac{t a n \frac{1}{x}}{\frac{1}{x}}}{- x 4 - \frac{1}{x} + \frac{1}{x ^{2}}}$
$= \frac{1}{- 4}$
$= - \frac{1}{2}$