List of top Engineering Mathematics Questions on Differentiation asked in GATE PE

Let \(f(x) = \ln x\). The first derivative \(f'(x)\) is to be calculated at \(x=1\) using numerical differentiation. \(f'(1)\) is calculated using: - First-order forward difference (\(f'_{FD}\)), - First-order backward difference (\(f'_{BD}\)), - Second-order central difference (\(f'_{CD}\)), with interval width \(h = 0.1\). The correct order of the values of \(f'_{FD}, f'_{BD}, f'_{CD}\) is:

Which of the following statement(s) is/are CORRECT?

Let \( f(x) = \ln x \). The first derivative \( f'(x) \) is to be calculated at \( x = 1 \) using numerical differentiation. \( f'(1) \) is calculated using first order forward difference (\( f'_{FD} \)), first order backward difference (\( f'_{BD} \)), and second order central difference (\( f'_{CD} \)), using interval width \( h = 0.1 \). The CORRECT order of the values of \( f'_{FD} \), \( f'_{BD} \), and \( f'_{CD} \) is: