Question

if
f(x)={x^2-1, x<3
2ax, x>=3}

what is the value of makes every x become continuous

Answer 1

what value of a is continuous at every x

Answer 2

a function is continuous if the left hand limit of 3 is equal to the right hand limit

Answer 3

so lim x->3 - would be: 3^2-1=9-1=8
lim x->3 + 2*a*3

Answer 4

by the way lim x->3+ (2*a*3), by that i meant lim as x goes to three from the right side

Answer 5

anyway both limits have to be equal so:
2*a*3 = 8
6a = 8
a = 8/6 = 4/3