Verified Solution • 2025–26 Session moderate

QJEEAdv24Ma4044: JEE Advanced 2024 Mathematics - Class 12 JEEAdv24Ma4044 Solution: Let . If , then the value of is

Let k∈Rk \in \mathbb{R} . If lim⁡x→0+(sin⁡(sin⁡kx)+cos⁡x+x)2x=e6\lim \limits_{x \rightarrow 0+}(\sin (\sin k x)+\cos x+x)^{\frac{2}{x}}=e^6 , then the value of kk is

Multiple Choice Options

  • A 1
  • B 2
  • C 3
  • D 4

Step-by-Step Verified Solution

limx→02x(sin⁡(sin⁡kx)+cos⁡x+x−1)=6limx→0sin⁡(sin⁡kx)⋅sin⁡kx(sin⁡kx)kx⋅k+1−limx→01−cos⁡xx2⋅x=3k+1=3⇒k=2

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