limx→ √2[(x²+x√2-4)/(x²-3x√2+4)]

7.2 Q.II · Q30

\displaystyle\lim_{x\to \sqrt2}\left[\frac{x^2+x\sqrt2-4}{x^2-3x\sqrt2+4}\right]

Maharashtra MsbshseTextbookSubjectiveImportance★★★★★est

50% · 69/137 Questions

🔒 Locked · start free trial →

You're viewing a preview — the full solution, concept, methods & PYQ mapping are locked.

Start your 14-day free trial to unlock the full solution →

$x^2+\sqrt2x-4$ factors (using the quadratic formula, roots $x=\sqrt2,-2\sqrt2$ ) as $(x-\sqrt2)(x+2\sqrt2)$ . $x^2-3\sqrt2x+4$ factors (roots $x=\sqrt2,2\sqrt2$ ) as $(x-\sqrt2)(x-2\sqrt2)$ . Cancelling $(x-\sqrt2)$ : $\ …

Start your 14-day free trial to unlock the full solution →

←Previous questionQ29 — limΔ x→ 0[((x+Δ x)²-2(x+Δ x)+1-(x²-2x+1))/(Δ x)]→Next questionQ31 — limx→ 2[(x³-7x+6)/(x³-7x²+16x-12)]

Q. $\displaystyle\lim_{x\to \sqrt2}\left[\frac{x^2+x\sqrt2-4}{x^2-3x\sqrt2+4}\right]$

Concept understanding — Limits by Factorization

Q.lim⁡x→2[x2+x2−4x2−3x2+4]\displaystyle\lim_{x\to \sqrt2}\left[\frac{x^2+x\sqrt2-4}{x^2-3x\sqrt2+4}\right]x→2​lim​[x2−3x2​+4x2+x2​−4​]

🎓Unlock everything free for 14 days

Q. $\displaystyle\lim_{x\to \sqrt2}\left[\frac{x^2+x\sqrt2-4}{x^2-3x\sqrt2+4}\right]$

Unlock everything free for 14 days