Verified Solution • 2025–26 Session moderate

QJEEM24Maa23f: JEE Main 2024 Mathematics - Class 12 JEEM24Maa23f Solution: Let be a differentiable function such that f ′ ( 1 ) = lim a →…

Let f:(−∞,∞)−{0}→Rf:(-\infty, \infty)-\{0\} \rightarrow \mathbb{R} be a differentiable function such that f′(1)=lima→∞a2f(1a). Then lima→∞a(a+1)2tan−1⁡(1a)+a2−2loge⁡a is equal to

Multiple Choice Options

  • A 52+π8\frac{5}{2}+\frac{\pi}{8}
  • B 38+π4\frac{3}{8}+\frac{\pi}{4}
  • C 34+π8\frac{3}{4}+\frac{\pi}{8}
  • D 32+π4\frac{3}{2}+\frac{\pi}{4}

Step-by-Step Verified Solution

Let f′(1)=kf^{\prime}(1)=k

⇒limx→0f(x)x2=k(00)

limx→0f′(x)2x=limx→0f′′(x)2=k⇒f′′(0)=2k

Given information is not complete.

Related Learning Resources & Exam Preparation

JEE Main PYQ Question Bank
Browse year-wise authentic previous years' questions with solutions
Authentic CBT Mock Tests
Simulate official exam environment with live timer and percentile scoring