Which of the following statements is true for the function f(x) = {x² + 3, x ≠ 0; 1, x = 0} ?
If x = e^(x/y), prove that dy/dx = (log x – 1)/(log x)²
Check the differentiability of f(x) = {x² + 1, 0 ≤ x < 1; 3 – x, 1 ≤ x ≤ 2} at x = 1.
Check for differentiability of the function f defined by f(x) = |x − 5|, at the point x = 5.
If y = (tan⁻¹x)², show that (x² + 1)² d²y/dx² + 2x(x² + 1) dy/dx = 2.
The greatest integer function defined by f(x) = [x], 1 < x < 3 is not differentiable at x =
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