The maximum value of fx = logxxx ≠ 0, x ≠ 1 is
e
1e
e2
1e2
If g(x) is the inverse function of f(x) and f'x = 11 + x4, then g'(x) is
1 + [g(x)]4
1 - [g(x)]4
1 + [f(x)]4
11 + g(x)4
The inverse of the matrix 10033052- 1 is
- 13- 30031092- 3
- 13- 3003- 10- 9- 23
- 133003- 10- 9- 23
- 13- 300- 3- 10- 9- 23
If the function f(x) = tanπ4 + x1x for x ≠ 0 is = K for x = 0 continuous at x = 0, then K = ?
e- 1
e- 2
For a invertible matrix A if A(adjA) = 100010 then A =
100
- 100
10
- 10
If x = f(t) and y = g(t) are differentiable functions of t, then d2ydx2 is
f't . g''t - g't . f''tf't3
f't . g''t - g't . f''tf't2
g't . f''t - f't . g''tf't3
g't . f''t + f't . g''tf't3
A.
Given, x = f(t) and y = g(t)On differentiating both sides w.r.t. 't', we getdxdt = f't and dydt = g'tWe know that, dydx = dydtdxdt⇒ dydx = g'tf'tAgain, differentiating both sides w.r.t. 'x', we getd2ydx2 = f't . g''t - g't . f''tf't2 . dtdxd2ydx2 = f't . g''t - g't . f''tf't3
If α and β are roots of the equation x2 + 5x - 6 = 0, then the value of tan-1α - tan-1β is
π2
0
π
π4
If the volume of spherical ball is increasing at the rate of 4π cm3/s, then the rate of change of its surface area when the volume is 288 π cm3, is
43π cm2/s
23π cm2/s
4π cm2/s
2π cm2/s
If f(x) = = logsec2xcot2x for x ≠ 0= K for x = 0 is continuous at x = 0, then K is
1
If the inverse of the matrix α14- 1231623 does not exist, then the value of α is
- 1
- 2