If limx→∞(11x^3-3x+4)/(13x^3-5x^2-7)=a/b then the value of a+b equals

Correct answer: (D) 24. limx→∞(11x^3-3x+4)/(13x^3-5x^2-7) limx→∞(x^311-3x^2+4x^3)/(x^313-5x-7x^3) limx→∞(11-3x^2+4x^3)/(13-5x-7x^3) x→∞⇒1/x→0 ⇒(11-0+0)/(13-0-0)=11/13 a=11,b=13 a+b=24.

Q102 / 160 · AP EAMCET 2021 (20 Aug Shift 2) · Mathematics

If $\lim_{x \to \infty} (\frac{11 x^{3} - 3 x + 4}{13 x^{3} - 5 x^{2} - 7}) = \frac{a}{b}$ then the value of $a + b$ equals

A
$11$
B
$13$
C
$8$
Correct answer
D
$24$

Solution

$\lim_{x \to \infty} \frac{11 x^{3} - 3 x + 4}{13 x^{3} - 5 x^{2} - 7}$

$\lim_{x \to \infty} \frac{x^{3} (11 - \frac{3}{x^{2}} + \frac{4}{x^{3}})}{x^{3} (13 - \frac{5}{x} - \frac{7}{x^{3}})}$

$\lim_{x \to \infty} \frac{11 - \frac{3}{x^{2}} + \frac{4}{x^{3}}}{13 - \frac{5}{x} - \frac{7}{x^{3}}}$

$x \to \infty \Rightarrow \frac{1}{x} \to 0$

$\Rightarrow \frac{11 - 0 + 0}{13 - 0 - 0} = \frac{11}{13}$

$a = 11, b = 13$

$a + b = 24$ .

Hence, the correct answer is option: 'D'.

If limx→∞11x3-3x+413x3-5x2-7=ab then the value of a+b equals

Solution

Relevant Questions

If $\lim_{x \to \infty} (\frac{11 x^{3} - 3 x + 4}{13 x^{3} - 5 x^{2} - 7}) = \frac{a}{b}$ then the value of $a + b$ equals