y=2x^(2)+3sin xquad (1)/(2)x=0

Find the slope of the tangent and normal to the following curve. (i) y = 2x^(2) + 3 sin x at x = 0 (ii) y = (sin 2x + cot x + 2)^(2) "at x" = (pi)/(2)

If sin y=x sin(y+a) and (dy)/(dx)=(A)/(1+x^(2)-2x cos a) ,then the value of A if x=0 and y=0 is (A) 2 (B) cos a (C) sin a (D) sin2a

Find lim{x rarr0}(2sin^(2)x+sin x-1)/(2sin^(2)x-3sin x+1)

2.The number of ordered pair(s) (x,y) satisfying y=2sin x and y=5x^(2)+2x+3 is equal to- (1)0(2)1(3)2(4)oo

If ((sin x)^(2y))/((cos x)^((2)/(2)))+((cos x)^(2y))/((sin x)^((2)/(2)))=sin2x for 0

If f(x)=(2x+3sin x)/(3x+2sin x),x!=0 is continuous at x=0, then find f(0)

If f(x)=(2x+3sin x)/(3x+2sin x),x!=0 is continuous at x=0, then find f(0)

If (2+sin x)(dy)/(dx)+(y+1)cos x=0 and y(0)=1, then y((pi)/(2)) is equal to -(1)/(3)(2)(4)/(3) (3) (1)/(3)(4)-(2)/(3)

The equation of the tangent to the curve y=(1+x)^(y)+sin^(-1)(sin^(2)x) at x = 0 is :a) x-y+1=0 b) x+y+1=0 c) 2x-y+1=0 d) x+2y+2=0

The value of lim _(x to 0) ( x ^(3) sin ((1)/(x)) - 2 x ^(2))/( 1 + 3x ^(2)) is