Algebraic Limits

JEE Main Mathematics · Limits · 4 questions, latest first

• For t>-1, let α_t and β_t be the roots of the equation ((t+2)^1 / 7-1) x^2+((t+2)^1 / 6-1) x+((t+2)^1 / 21-1)=0. If lim_t →-1^+…20257 April, Shift 2 · Q23
• lim_x → 0 cosec x(√(2 cos^2 x+3 cos x)-√(cos^2 x+ sin x+4)) is:202524 January, Shift 1 · Q12
• If lim_x → 1 ((5 x+1)^1 / 3-(x+5)^1 / 3)/((2 x+3)^1 / 2-(x+4)^1 / 2)=(m √5)/(n(2 n)^2 / 3), where gcd(m, n)=1, then 8 m+12 n is…20244 April, Shift 1 · Q24
• If a= lim_x → 0 (√(1+√(1+x^4))-√2)/x^4 and b= lim_x → 0 (sin^2 x)/(√2-√(1+ cos x)), then the value of ab^3 is:202427 January, Shift 1 · Q9