defence exam Agniveer Vayu Group X & XY Mock Test 01/2026 Mathematics Differential Calculus Differentiability
If \( f(x) \) is a differentiable function in the interval \( (0, \infty) \) such that
\( f(1) = 1 \) and \( \lim_{t\rightarrow x} \dfrac {t^{2}f(x) - x^{2}f(t)}{t - x} = 1 \), for each \( x > 0 \), then \( f\left (\dfrac {3}{2}\right ) \) is equal to:
1
\( \dfrac {25}{9} \)
2
\( \dfrac {23}{18} \)
3
\( \dfrac {13}{6} \)
4
\( \dfrac {31}{18} \)