If `y=a e^(m x)+b e^(-m x),` then `(d^(2y))/(dx^2)-m^2y` is equal to `m^2(a e^(m x)-b e^(-m x))` `1` (c) 0 (d) none of these

If y= 500e^(7x) +600e^(-7x) , show that (d^(2)y)/(dx^(2))= 49y .

If y=500e^(7x)+600e^(-7x) show that (d^(2)y)/(dx^(2))=49y .

If y=a x^(n+1)+b x^(-n),t h e nx^2(d^2y)/(dx^2) is equal to n(n-1)y (b) n(n+1)y (c) n y (d) n^2y

If e^y(x+1)=1 , show that (d^2y)/(dx^2)=((dy)/(dx))^2

If y= 3e^(2x)+2e^(3x) , prove that (d^(2)y)/(dx^(2))-5(dy)/(dx)+6y=0 .

If ln((e-1)e^(xy) +x^2)=x^2+y^2 then ((dy)/(dx))_(1,0) is equal to

The value of int_0^1e^(x^2-x)dx is (a) 1 (c) > e^(-1/4) (d) none of these

If x^2+y^2+z^2=r^2,t h e ntan^(-1)((x y)/(z r))+tan^(-1)((y z)/(x r))+tan^(-1)((x z)/(y r)) is equal to (a) pi (b) pi/2 (c) 0 (d) none of these

If a x+b y=1 is tangent to the hyperbola (x^2)/(a^2)-(y^2)/(b^2)=1 , then a^2-b^2 is equal to 1/(a^2e^2) (b) a^2e^2 b^2e^2 (d) none of these

For x in R , lim_(xrarroo)((x-3)/(x+2))^x is equal to (a) e (b) e^(-1) (c) e^(-5) (d) e^5