[" (8) "y=log_(10)sin(x-3)+sqrt(16)-x],[y=sqrt(x^(2)+3x+2)+(1)/(sqrt(3+2x))]

Find the domains of definition of the following functions: (a) y=(2x-3)/sqrt(x^(2)+2x+3) (b) y=log sin(x-3) +sqrt(16-x^(2)) , (c) y=sqrt(3-x) +arc cos ""(x-2)/(3) (d) y=x/(log (1+x))

The domain of the function f(x)=log_(10) sin(x-3)+sqrt(16-x^(2)) is

Find common tangent of the two curve y^(2)=4x and x^(2)+y^(2)-6x=0 (a) y=(x)/(3)+3 (b) y=((x)/(sqrt(3))-sqrt(3)) (c) y=(x)/(3)-3 (d) y=((x)/(sqrt(3))+sqrt(3))

Find common tangent of the two curve y^(2)=4x and x^(2)+y^(2)-6x=0 (a) y=(x)/(3)+3 (b) y=((x)/(sqrt(3))-sqrt(3)) (c) y=(x)/(3)-3 (d) y=((x)/(sqrt(3))+sqrt(3))

Find common tangent of the two curve y^(2)=4x and x^(2)+y^(2)-6x=0 (a) y=(x)/(3)+3 (b) y=((x)/(sqrt(3))-sqrt(3)) (c) y=(x)/(3)-3 (d) y=((x)/(sqrt(3))+sqrt(3))

Find the greatest & least value of f(x)=sin^(-1).(x)/(sqrt(x^(2)+1))-ln x in [(1)/(sqrt(3)), sqrt(3)] .

If quad (x^(2))/(2)+(1)/(2)x sqrt(x^(2)+1)+log_(e)sqrt(x+sqrt(x^(2)+1))y=(x^(2))/(2)+(1)/(2)x sqrt(x^(2)+1)+log_(e)sqrt(x+sqrt(x^(2)+1)) prove that 2y=xy'+log_(e)y', where y' denotes the derivative w.r.x.

Find the domain of the following: (i) f(x) = (1)/(log_(10) (1-x)) + sqrt(x+2) (ii) f(x) = sqrt(1-2x) + 3 sin^(-1) ((3x-1)/(2))

The area bounded by the curves xsqrt3+y=2log_(e)(x-ysqrt3)-2log_(e)2, y=sqrt3x, y=-(1)/(sqrt3)x+2, is

The area bounded by the curves xsqrt3+y=2log_(e)(x-ysqrt3)-2log_(e)2, y=sqrt3x, y=-(1)/(sqrt3)x+2, is