Question

Assertion :$\underset{x\to \infty }{lim}\frac{2x^3+3x^2-4x+7}{3x^3+4x^2-x-9}=\frac{2}{3}$ Reason: If p(x) & q(x) are polynomials then $\underset{x\to \infty }{lim}\frac{p\left(x\right)}{q\left(x\right)}$ is a finite non zero number if degree of p(x)=degree of q(x).

• A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
• B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
• C. Assertion is correct but Reason is incorrect
• D. Both Assertion and Reason are incorrect

Answer 1

The correct option is A Both Assertion and Reason are correct and Reason is the correct explanation for Assertion

$\underset{x\to \infty }{lim}\frac{2x^3+3x^2-4x+7}{3x^3+4x^2-x-9}$ $($ dividing by $x^3$ in numerator and denominator $)$

$=\underset{x\to \infty }{lim}\frac{2+\frac{3}{x}-\frac{4}{x^2}+\frac{7}{x^3}}{3+\frac{4}{x}-\frac{1}{x^2}-\frac{9}{x^3}}$

$=\frac{2+0-0+0}{3+0-0-0}=\frac{2}{3}$