JEE Main Mathematics — Limits Previous-Year Questions

If x → ₀ e⁽a⁻¹⁾ x+2 ~b x+(c-2) e⁻xx x- e(1+x)=2, then a²+b²+c² is equal to :

Let f: R →(0, ∞) be a twice differentiable function such that f(3)=18, fⁱme(3)=0 and fⁱme ⁱme(3)=4. Then x → ₁ ( e ((f(…

If → ₂ (x³ - 5x² + ax + b)(√(x-1) - 1)(x-1) = m, then a + b + m is equal to :

Let f(x) = → ₀ ((1 - (xy)) (xy))/(y³). Then the number of solutions of the equation f(x) = x, x R is :

The value of → ₀ ((x²² x)/(x² - ² x) ) is:

The product of all possible values of α, for which → ₀ ((1 - (α x)((α+1)x)((α+2)x))/(²((α+1)x)) ) = 2, is:

Let → ₂ (((x-2))(rx² + (p-2)x - 2p))/((x-2)²) = 5 for some r, p R. If the set of all possible values of q, such that th…

Let [·] denote the greatest integer function and f(x)= n → ∞ 1n³ ₌₁ⁿ [k²3x ]. Then 12 ₌₁\ⁱⁿfty f(j) is equal to \\\\_.

The value of x → ₀ e ( (e x) · (e² x ) · … · (e¹⁰ x ) )e²-e² x is equal to

x → ∞ (2 x²-3 x+5 )(3 x-1)⁽x⁾/⁽²⁾ (3 x²+5 x+4 ) √((3 x+2)^x) is equal to :