If z = sec-1x4 + y4 - 8x2y2x2 + y2, then x∂z∂y + y∂z∂y is equal to
cotz
2cotz
2tanz
2secz
If f : R → R is defined byf(x) = 2sinx - sin2x2xcosx, if x ≠ 0, a , if x = 0, then the value of a so that f is continuous at 0 is
2
0
1
x = cos-111 + t2, y = sin-1t1 + t2 ⇒ dydx = ?
tan(t)
sin(t)cos(t)
ddxa tan-1x + blogx - 1x + 1 = 1x4 - 1 ⇒ a - 2b = ?
- 1
y = easin-1x ⇒ 1 - x2yn + 2 - 2n + 1xyn + 1 is equal to
-n2 + a2yn
n2 - a2yn
n2 + a2yn
-n2 - a2yn
If f : R → R defined byf(x) = 1 + 3x2 - cos2xx2, for x ≠ 0k, for x= 0is continuous at x = 0, then k is equal to
5
6
If f(x) = cosxcos2x. . . cosnx, then f'(x) + ∑r = 1n rtanrxfx = ?
f(x)
- f(x)
2f(x)
If y = cos-1a2 - x2a2 + x2 + sin-12axa2 + x2,then dydx = ?
ax2 + a2
2ax2 + a2
4ax2 + a2
a2x2 + a2
If fx = sinx + cosx,then fπ4fivπ4 = ?
3
4
B.
f(x) = sinx + cosxf'(x) = cosx - sinxf''(x) = - sinx - cosxf'''(x) = - cosx + sinxf''''x = sinx + cosxSo, fπ4 = f''''π4 = sinπ4 + cosπ4 = 12 + 12 = 22 = 2Then, fπ4 f''''π4 = 2 × 2 = 2
If y = sinmsin-1x, then 1 - x2y2 - xy1 = ?Here, yn denotes dnydxn
m2y
- m2y
2m2y
- 2m2y