lf the rate of change of volume of sphere is equal to the rate of change of its radius, then its radius is equal to ____________

The distance moved by the particle in time t is given by \(x=t^{3}-12 t^{2}+6 t+8\). At the instant when its acceleration is zero, the velocity is ____________

The statement "If f has a local extremum at c and if f'(c) exists then f'(c) = 0" is ________

\(\underset { x\rightarrow 0 }{ lim } \frac { x }{ tanx } \) is _________

The curve y = e^x is ________

If x + y = 8, then the maximum value of xy is _________

The function f(x) = x⁹ + 3x⁷+ 64 is increasing on ________

The function -3x+12 is ________ function on R.

If the curves y = 2e^x and y = ae^-x intersect orthogonally, then a = _________

If the slope of the curve 2y² = ax²+b at (1,-1) is - 1, then the values of a, b is __________

In LMV theorem, we have f'(x₁) = \(\frac { f(b)-f(a) }{ b-a } \) then a < x₁ _________

The equation of the tangent to the curve x = t cost, y = t sin t at the origin is __________

The critical points of the function f(x) = \((x-2)^{ \frac { 2 }{ 3 } }(2x+1)\) are __________

The angle made by any tangent to the curve y = x⁵ + 8x + 1 with the X-axis is a __________

The value of \(\underset { x\rightarrow \infty }{ lim } { e }^{ -x }\) is __________