If w is a cube root of unity, then 1ww2ww21w21w is equal to
1
w
w2
0
The domain of definition of function fx = 1 + 2x + 4- 0.52 - x + 4- 0.5 + x + 40.5 + 4x + 40.5 is
R
(- 4, 4)
R+
- 4, 0 ∪ 0, ∞
The set of points where the functton f(x) = xx is differentiable is
- ∞, ∞
- ∞, 0 ∪ 0, ∞
0, ∞
If fx = 1 - sinxπ - 2x2 . logsinxlog1 + π2 - 4πx + 4x2, x ≠ π2k , x = π2 is continuous at x = π2, then k is equal to
- 116
- 132
- 164
- 128
If y = 4x - 5 is a tangent to the curve y2 = px3 + q at (2, 3), then
p = 2, q = - 7
p = - 2, q = 7
p = - 2, q = - 7
p = 2, q = 7
On which of the following intervals is the function f(x) = 2x2 - logx, x ≠ 0 increasing 2.
12, ∞
- ∞, - 12 ∪ 12, ∞
- ∞, - 12 ∪ 0, 12
- 12, 0 ∪ 12, ∞
The greatest value of f(x) = (x + 1)1/3 - (x - 1)1/3 on [0, 1] is
2
3
13
∫xe - 1 + ex - 1xe + exdx is equal to
1elogxe - ex + c
1elogxe + ex + c
1elogex - xe + c
None of the above
∫01dx1 + x + x is equal to
432 - 1
342 - 1
431 - 2
341 - 2
A.
I = ∫01dx1 + x + x = ∫011 + x - x1 + x + x1 + x - xdx = ∫011 + x + x1 + x - xdx = ∫011 + x12 - ∫01x12dx = 1 + x323201 - x323201 = 23232 - 1 - 231 - 0 = 2322 - 1 - 23 = 2322 - 1 - 1 = 2322 - 2 = 432 - 1
∫015x - 3dx is equal to
1013
3110
1310
None of these