In Differential Calculus by Arihant Publication
Pg.no. 88 - Q.no. 2,3,5
Pg.no. 90 - Q.no. 15,17
Pg.no. 91 - Q.no. 29
FOR THOSE WHO DONT HAVE THIS BOOK:
NOTE:
D is same as (d/dx)
f(-1)(x) is same as f inverse of x
^3 means 'power 3'
'pi' is same as 22/7 or 3.14
'sqrt.' is same as square root of
1) Let f(x) = (2x-pi)^3 + 2x - cosx. The value of D(f(-1)(x)) at x = pi is:
a) 3 pi^2 + 2
b) -2
c) 1/(3pi^2 + 2)
d) 1/3
2) A function f:R->R satisfies
sinx cosy (f(2x+2y) - f(2x-2y)) = cosx siny (f(2x+2y) + f(2x- 2y)). If f'(0)=1/2, then:
a) f''(x) - f'(x) =0
b) 4f''(x) + f(x) =0
c) f''(x) + f(x) =0
d) 4f''(x) - f(x) =0
3. If y= sec(-1)((x-1)/(x+1)) + sin(-1)((x-1)/(x+1)), then Dx=?
a) 1 b) 0
c) (x-1)/(x+1) d) (x+1)/(x-1)
4. If sqrt.(x^2 + y^2) = a e^(tan(-1)(y/x)), a>0 then y''(0) is:
a)(a/2) e^(-pi/2) b) a e^(pi/2)
c)(-2 e^(-pi/2))/a d) does not exist
5. If P(x) is a polynomial such that P(x^2+1)={P(x)}^2 + 1 and P(0)=0 then P'(0) is equal to:
a) 1 b)0
c) -1 d)none of these
6)Let f:R->R be a differential function satisfying f(y).f(x-y)=f(x) for all x,y and f'(5)=q and p.f(0)=f'(0) then f(5) is:
a) p^2/q b) p/q
c) q/p d) q.
Please help me askIITians.
In Differential Calculus by Arihant Publication
Pg.no. 88 - Q.no. 2,3,5
Pg.no. 90 - Q.no. 15,17
Pg.no. 91 - Q.no. 29
FOR THOSE WHO DONT HAVE THIS BOOK:
NOTE:
D is same as (d/dx)
f(-1)(x) is same as f inverse of x
^3 means 'power 3'
'pi' is same as 22/7 or 3.14
'sqrt.' is same as square root of
1) Let f(x) = (2x-pi)^3 + 2x - cosx. The value of D(f(-1)(x)) at x = pi is:
a) 3 pi^2 + 2
b) -2
c) 1/(3pi^2 + 2)
d) 1/3
2) A function f:R->R satisfies
sinx cosy (f(2x+2y) - f(2x-2y)) = cosx siny (f(2x+2y) + f(2x- 2y)). If f'(0)=1/2, then:
a) f''(x) - f'(x) =0
b) 4f''(x) + f(x) =0
c) f''(x) + f(x) =0
d) 4f''(x) - f(x) =0
3. If y= sec(-1)((x-1)/(x+1)) + sin(-1)((x-1)/(x+1)), then Dx=?
a) 1 b) 0
c) (x-1)/(x+1) d) (x+1)/(x-1)
4. If sqrt.(x^2 + y^2) = a e^(tan(-1)(y/x)), a>0 then y''(0) is:
a)(a/2) e^(-pi/2) b) a e^(pi/2)
c)(-2 e^(-pi/2))/a d) does not exist
5. If P(x) is a polynomial such that P(x^2+1)={P(x)}^2 + 1 and P(0)=0 then P'(0) is equal to:
a) 1 b)0
c) -1 d)none of these
6)Let f:R->R be a differential function satisfying f(y).f(x-y)=f(x) for all x,y and f'(5)=q and p.f(0)=f'(0) then f(5) is:
a) p^2/q b) p/q
c) q/p d) q.
Please help me askIITians.
