find the constants a and b such that the function is continuous on the entire real line. f(x)=x^3 when x is less than of equal to 2 and ax^2 when x2

Question

find the constants a and b such that the function is continuous on the entire real line. f(x)=x^3 when x is less than of equal to 2 and ax^2 when x>2

anonymous · Answer

less than or equal to 2*

waleed_imtiaz · Answer

Where is the constant b  in the function ?

anonymous · Answer

ohh there are multiple problems. there is only a in this one

waleed_imtiaz · Answer

First we have to define the function at a constant number.... Here it is 2..so where x=2 the function is  f(x)=x^3; f(2)=2^3=8....
now take L.H.L. (left hand limit ,where x is less than 2)= f(x)=x^3=2^3=8...
now take R.H.L. (right hand limit, where x is greater than 2)=f(x)=ax^2=a(2)^2=4a.....
as the function is continuous..... So f(c) means function defined at a constant number should equal to the limits... (L.H.L and R.H.L.) 
so 8=4a
so a =2
I wanted u to solve the problem... but if u still have some problem, then ask me........