If A = 110215121, then a11A21 + a12A22 + a13A23 is equal to
1
0
- 1
2
If Rolle's theorem for f(x) = exsinx - cosx is verified on π4, 5π4, then the value of c is
π3
π2
3π4
π
If 2tan-1cosx = tan-12cscx, then sinx + cosx is equal to
22
12
The approximate value of f(x) = x3 + 5x2 - 7x + 9 at x = 1.1 is
8.6
8.5
8.4
8.3
The point on the curve 6y = x3 + 2 at which y-coordinate is changing 8 times as fast as x-coordinate is
(4, 11)
(4, - 11)
(- 4, 11)
(- 4, - 11)
If the function f(x) defined by
fx = xsin1x, for x ≠ 0k, for x = 0
is continuous at x = 0, then k is equal to
If y = emsin-1x and 1 - x2dydx2 = Ay2, then A is equal to
m
- m
m2
- m2
tan-13 - sec-1- 2csc-1- 2 + cos-1- 12 is equal to
45
- 45
35
For what value of k, the function defined by
f(x) = log1 + 2xsinx°x2, for x ≠ 0k , for x = 0
is continuous at x = 0 ?
π90
90π
If log10x2 - y2x2 + y2 = 2, then dydx is equal to
- 99x101y
99x101y
- 99y101x
99y101x
A.
Given, log10x2 - y2x2 + y2 = 2⇒ x2 - y2x2 + y2 = 102⇒ x2 - y2 = 100x2 + y2On differentiating both sides, we get 2x - 2ydydx = 1002x + 2ydydx⇒ x - ydydx = 100x + 100ydydx⇒ 101ydydx = - 99x⇒ dydx = - 99x101y