Thread: continuity and limits

consdier the function:

f(x) = (sin3x)/x , x<0
a + 1 , x=0
be^(-2x), x>0

a.)explain why f(x) is continuous for all real x =/ 0 (=/ mean does not equal..sry dunno how to type the sign)

b.)using limits, determine the values of a and b that make f(x) continuous at x = 0

plz help!
thx

Originally Posted by ssdimensionss

consdier the function:

f(x) = (sin3x)/x , x<0
a + 1 , x=0
be^(-2x), x>0

a.)explain why f(x) is continuous for all real x =/ 0 (=/ mean does not equal..sry dunno how to type the sign)

b.)using limits, determine the values of a and b that make f(x) continuous at x = 0

plz help!
thx

a.) Use the known properties of each function.

b.) You need to solve:

1. .

2. .

I hope calculating the two limits is routine for you.

how do u solve the limit x app 0 sin(3x)/x ? coz if i use sandwich rule the limit does not exist?
thx

Originally Posted by ssdimensionss

how do u solve the limit x app 0 sin(3x)/x ? coz if i use sandwich rule the limit does not exist?
thx

Substitute t = 3x:

.

It would be expected that you know and that you can do basic algebraic manipulations of this limit.