Question

I've been asked to figure out why sin(x)/x=1 is false when it's not a limit...

is it because the only time sin(x)=x is when x=0, and you can't divide by 0? or is there something more tricky?

Answer 1

yes you are right it is only true when x=0 but sin(0)/0 is indeterminate so it has no value but we know the limit is 1

Answer 2

when its a limit you can use l'hopitals thereom which simplifies the expression to cos(x)=1 which solution is then x=0.

Answer 3

the limit = 1, but my professor wants to know why it doesn't equal 1 when it isn't a limit

Answer 4

so, i'm on the right track?

Answer 5

this is because you cannot have sin(0)/0 in reality. but when its a limit you can see it tends to it. you cant divide by 0 in reality even though you know the answer. hard to see around i guess

Answer 6

but yeah you are

Answer 7

thanks!