Why is this incorrect?

[jtw2e2]

Hi, well I've finally moved up from the PreCalc thread.

I'm wondering why in this particular problem it is not correct to directly substitute in -3? When I do so, obviously the numerator is 0, and 0/anything = 0, so I would expect the limit = 0. But according to the book the answer is 6/5. What am I missing here? Thanks in advance.

 

[daon]

0/anything is zero, but only when "anything" is not zero.

instead, factor the denominator and cancel any repeat factors (in this case you'll be cancelling x+3).

 

[jtw2e2]

0/anything is zero, but only when "anything" is not zero.

instead, factor the denominator and cancel any repeat factors (in this case you'll be cancelling x+3).

Thanks, I always do stupid things. So, just to be clear, had the denominator been anything other than 0 with initial direct substitution, that resulting limit would have been correct and I would not have to do the factoring, right?

 

[daon]

0/anything is zero, but only when "anything" is not zero.

instead, factor the denominator and cancel any repeat factors (in this case you'll be cancelling x+3).

Thanks, I always do stupid things. So, just to be clear, had the denominator been anything other than 0 with initial direct substitution, that resulting limit would have been correct and I would not have to do the factoring, right?

yup. if the function is continuous (i.e. you don't get things like 0 in the denominator), the function's limit IS the function's value.