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Which of the following statements is true for the function f(x) = {x² + 3, x ≠ 0; 1, x = 0} ?
Check whether the function f(x) = x² |x| is differentiable at x = 0 or not.
If y = √(tan √x), prove that √x (dy/dx) = (1 + y⁴)/(4y).
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.
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