The equation sinx + 2sin2x + 3sin3x = 8π has atleast one root in
π, 3π2
0, π2
π2, π
π2, 3π4
If xy = ey - x, then dydx =
yx - 1xy + 1
yx + 1xy - 1
x + 1y - 1
x - 1y + 1
If y = cos-1sinx + cosx2, - π4 < x < π4, then dydx =
- 1
1
0
None of these
limx→∞x + ax + ba + b is equal to
1b - a
ea - b
eb
limx→0x . 10x - x1 - cosx is equal to
log10
2log10
3log10
4log10
B.
limx→0x . 10x - x1 - cosxUsing L-Hospital's rule= limx→0x10xlog10 + 10x - 1sinxAgain using L-Hospital's rule= limx→0x10xlog102 + 10xlog10 + 10xlog10cosx= 0 + log10 + log10cos0= 2log10
If yk is the kth derivative of y with respect to 'x', and y = cos(sin(x)), then y1sinx + y2cosx is equal to
ysin3x
- ysin3x
ycos3x
- ycos3x
limx→0sinxsin-1xx2 is equal to
∞
If a > 0, limx→a ax - xaxx - aa = - 1, then a is equal to :
e
2e
The value of limn→∞1n3∑k=1nk2x is
x
x2
x3
x4
If f: R → R is an even function having derivatives of all orders, then an odd function among the following is
f''
f'''
f' + f''
f'' + f'''