`sqrt(a^(2)x^(2)+2abx+b^(2))` = ……………..

Solve sqrt(2)x^(2) +x + sqrt(2)=0

Evaluate lim_(x to oo ) [sqrt(a^(2)x^(2)+ax+1)-sqrt(a^(2)x^(2)+1)].

lim_(xto0)(sqrt(x^(2)+a^(2))-a)/(sqrt(x^(2)+b^(2))-b)

If Lim_(x rarr a) (sqrt(x-b)-sqrt(a-b))/(x^(2)-a^(2))(a gt b) = 1/64 and Lim_(x rarr oo) (sqrt(x^(2)+ax)-sqrt(x^(2)+bx)) = 2 then the value of a/b, is

Let f(x) = - (x)/(sqrt(a^(2) + x^(2)))- (d-x)/(sqrt(b^(2) + (d-x)^(2))), x in R , where a, b and d are non-zero real constants. Then,

Prove that the product of the lengths of the perpendiculars drawn from the points (sqrt(a^(2)-b^(2)), 0) and (-sqrt(a^(2)-b^(2)), 0) to the line (x)/(a)cos theta+(y)/(b)sin theta=1 is b^(2)

Two parallel lines lying in the same quadrant make intercepts a and b on x and y axes, respectively, between them. The distance between the lines is (a) (ab)/sqrt(a^2+b^2) (b) sqrt(a^2+b^2) (c) 1/sqrt(a^2+b^2) (d) 1/a^2+1/b^2

Prove that the product of the lengths of the perpendiculars drawn from the points (sqrt(a^(2) - b^(2)) , 0) " and " (- sqrt(a^(2) - b^(2)), 0) to the line x/a cos theta + y/b sin theta = 1 " is " b^(2) .