Quantrex Quantrex AcademyJEE · NEET · NDA PYQs with solutions Open app
NTA Abhyas 2020
Exam
NTA Abhyas
Year
2020
Subject
Mathematics
Chapter
Limits

NTA Abhyas 2020 · Mathematics · Limits

If _ x → 0 ( ( a - n ) nx - tan x)sinnx x2 = 0, where n is a non...

If lim⁡x→0((a−n)nx−tan x)sinnxx2=0,\lim_{\text{x} \to 0}\dfrac{( ( a - n ) nx - \text{tan x)sin}\text{nx}}{\text{x}2} = 0\text{,} where nn is a non zero real number, then aa is equal to

Options

  1. A00
  2. Bn+1n\dfrac{\text{n} + 1}{\text{n}}
  3. Cnn
  4. Dn+1n\text{n} + \dfrac{1}{\text{n}}

Correct answer

D. n+1n\text{n} + \dfrac{1}{\text{n}}

Step-by-step solution

lim⁡x→0((a−n)nx−tan x)sinnxx2=0\lim_{\text{x} \to 0}\dfrac{( ( a - n ) n\text{x} - \text{tan x)sin}\text{nx}}{\text{x}2} = 0

⇒ \lim_{\text{x} \to 0} \left(\left(\text{a} - \text{n}\right) \text{n} - \dfrac{\text\tan \text{x}}{\text{x}}\right) \dfrac{\text\sin \text{nx}}{\text{x}} = 0

⇒((a−n)n−1)n=0⇒ \left(\left(\text{a} - \text{n}\right) \text{n} - 1\right) \text{n} = 0

⇒(a−n)n−1=0(∵n≠0)⇒ \left(\text{a} - \text{n}\right) \text{n} -1 = 0\left(∵ \text{n} \ne0\right)

∴a=n+1n∴ \text{a} = \text{n} + \dfrac{1}{\text{n}}
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 NTA Abhyas JEE Main PYQs