Quantrex Quantrex AcademyJEE · NEET · NDA PYQs with solutions Open app
JEE Main 20207 JanuaryMorning Shift
Exam
JEE Main
Year
2020
Date
7 January
Shift
Morning Shift
Subject
Mathematics
Chapter
Limits

JEE Main 2020 · 7 January · Morning Shift · Mathematics · Limits

_ x → 2 3 ^ x + 3 ^ 3 - x - 12 3 ^ - (x)/(2) - 3 ^ 1 - x is equal to

lim⁡x→23x+33−x−123−x2−31−x\lim_{x \to 2}\dfrac{{3}^{x} + {3}^{3 - x} - 12}{{3}^{- \dfrac{x}{2}} - {3}^{1 - x}} is equal to

Correct answer

0

Step-by-step solution

Let, 3x2=t,x→2⇒t→33\dfrac{x}{2} = t, x \to 2 ⇒ t \to 3

lim⁡t→3t2+27t2−121t−3t2=lim⁡t→3t4+27−12t2t−3\lim_{t \to 3}\dfrac{{t}^{2} + \dfrac{27}{{t}^{2}} - 12}{\dfrac{1}{t} - \dfrac{3}{{t}^{2}}} = \lim_{t \to 3}\dfrac{{t}^{4} + 27 - 12{t}^{2}}{t - 3}

lim⁡t→3(t2−3)(t+3)(t−3)(t−3)=6×6=36\lim_{t \to 3}\dfrac{\left({t}^{2} - 3\right)\left(t + 3\right)\left(t - 3\right)}{\left(t - 3\right)} = 6 \times 6 = 36

Practice Limits on Quantrex Academy →

More from Limits

Let _ x → 2 (( (x-2))(rx^2 + (p-2)x - 2p))/((x-2)^2) = 5 for some r, p ∈ ℝ . If the set… JEE Main 2026The value of _ x → 0 ((x^2 ^2 x)/(x^2 - ^2 x)) is: JEE Main 2026Let f(x) = _ y → 0 ((1 - (xy)) (xy))/(y^3) . Then the number of solutions of the equation… JEE Main 2026The product of all possible values of α , for which _ x → 0 ((1 - (α x) ((α+1)x)… JEE Main 2026If _ x → 2 (x^3 - 5x^2 + ax + b) ( x-1 - 1) _e(x-1) = m , then a + b + m is equal to : JEE Main 2026The value of _ x arrow 0 _ e ( (e x) · (e^ 2 x) · … · (e^ 10 x)) e^ 2 -e^ 2 x is equal to JEE Main 2026If _ x arrow 0 e^ (a-1) x +2 ~b x+(c-2) e^ -x x x- _ e (1+x) =2 , then a^ 2 +b^ 2 +c^ 2… JEE Main 2026Let [·] denote the greatest integer function and f(x)= _ n arrow ∞ 1 n^ 3 ∑_ k=1 ^ n [ k^… JEE Main 2026Let f: R arrow(0, ∞) be a twice differentiable function such that f(3)=18, f^ (3)=0 and… JEE Main 2026Let α and β be the real numbers such that _ x arrow 0 (1)/(x^3)((α)/(2) ∫_0^x (1)/(1-t^2)… JEE Advanced 2025Let x_0 be the real number such that e^ x_0 +x_0=0 . For a given real number α , define… JEE Advanced 2025Given below are two statements : Statement I : _ x arrow 0 ( ^ -1 x+ _e (1+x)/(1-x) -2 x… JEE Main 2025If the function f(x)=( ( x)- ( x))/( x- x) is continuous at x=0 , then f(0) is equal to… JEE Main 2025_ x arrow 0^ + (5(x)^ (1)/(3) ) _e(1+3 x^2) ( ^ -1 3 x )^2(e^ 5(x)^ (4)/(3) -1) is equal… JEE Main 2025If _ x arrow 1^ + ((x-1)(6+λ (x-1))+μ (1-x))/((x-1)^3)=-1 , where λ, μ ∈ ℝ , then λ+μ is… JEE Main 2025If Lim_ x arrow 0 (( x)/(x))^ (1)/(x^2) =p , then 96 _e p is equal to ______ JEE Main 2025 Full Limits list Limits JEE Maths PYQsJEE Mathematics PYQs All JEE Main PYQs