(4)/(2)(ax+b)^(2)

If (1)/((ax+b)(cx+d))+(A)/(ax+b) + (B)/(cx+d) then show that (1)/((ax+b)^(2)(cx+d))=(A)/((ax+b)^(2))+(AB)/(ax+b)+(B^(2))/(cx+d) .

If (1)/((ax+b)(cx+d))=(A)/(ax+b) + (B)/(cx+d) then show that (1)/((ax+b)^(2)(cx+d))=(A)/((ax+b)^(2))+(AB)/(ax+b)+(B^(2))/(cx+d) .

The coefficient of x^(n) in 1+(ax+b)+((ax+b)^(2))/(2!)+((ax+b)^(3))/(3!)+....

Which of the following pair(s) of curves is/are orthogonal? y^(2)=4ax;y=e^(-(1)/(2))y^(2)=4ax;x^(2)=4ayat(0,0)xy=a^(2);x^(2)-y^(2)=b^(2)y=ax;x^(2)+y^(2)=c^(2)

Statement 1: The line ax+by+c=0 is a normal to the parabola y^(2)=4ax. Then the equation of the tangent at the foot of this normal is y=((b)/(a))x+((a^(2))/(b)). Statement 2: The equation of normal at any point P(at^(2),2at) to the parabola y^(2)= 4ax is y=-tx+2at+at^(3)

Solve the following quadratic equation for x.x^(2)-4ax-b^(2)+4a^(2)=0

x^(2)-2ax-(4b^(2)-a^(2))=0

Solve each of the following quadratic equations: x^(2)-2ax-(4b^(2)-a^(2))=0

Solve the following quadratic equation by factorization method: ( ) x^(2)-2ax+a^(2)-b^(2)=0(ii)x^(2)-4ax+4a^(2)-b^(2)=0(iii)4x^(2)-4ax+(a^(2)-b^(2))=0(iv)4x^(2)-4a^(2)x+(a^(4)-b^(4))=

If lim_(x rarr oo)(sqrt(x^(4)-x^(2)+1)-ax^(2)-b)=0 then there existat least one a and b for which point (a,-4b) lies on the line