if lim x tends to 0 (x^-3sin3x + ax^-2 + b) exists and is equal to zero then find value of a and b.. need the procedure pls

No.. Actually this is the question lt_x→ ₀  x^-3Sin3x + ax^-2 + b 

Take the equation as (sin3x+ ax+ bx³)/x³  use l’hospitals rule and differentiate the following equation . you get

(3cos3x+ a+3bx²)/(3x² )

Use l’hospital’s rule again         (-9sin3x+ 6bx)/6x

Use l’hospital’s rule again            (-27cos3x+ 6b)/6

Now put x=0 and you get -27+6b=0 or b =27/6. .....

b=o