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
A.
Given, f(x) = x3 + 5x2 - 7x + 9On differentiating both sides w. r. t. x, we getf'(x) = 3x2 + 10x - 7Let x = 1 and ∆x = 0.1, so thatfx + ∆x = f1 + 0.1 = f1.1We know that,fx + ∆x = fx + ∆xf'x = x3 + 5x2 - 7x + 9 + ∆x × 3x2 + 10x - 7Put x = 1 and ∆x = 0.1, we get
f 1 + 0.1 = 13 + 512 - 71 + 9 + 0.1 × 3 × 12 + 10 × 1 - 7⇒ f1.1 = 1 + 5 - 7 + 9 + 0.13 + 10 - 7 = 8 + 0.16 = 8 + 0.6 = 8.6
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