Q3 (a) Let f be differential. Define a function f* by the equation f*(x) = lim f(x+4x)-f(x-4x) Ax-0 Ax Find the relationship between f* and f. (b). Show that a differentiable function f (x) is continuous, i.e., lim f(x + Ax) = f(x) . Ax-0 Q4. Determine whether the function is differentiable at x = 0. f (x ) = 1x, if x is rational if x is irrational Q5. Calculate the derivative of the given function, using the appropriate formula from the differential rules. (i) (x100 + 2x50 - 3) (7x8 + 20x + 5) -x+2 (ii) x3+7 (iii) 3x +x5-2x4+x-3 (iv) sin x x (v) sin (5x + 4) (vi) 2 tan() - 5 (vii) tan x - secx Q6. Using Chain rule, find the derivative of (i) x+2 3 (ii) V3x (iii) V (1 + x2)4 x