Question

lim x -> 0 (x-1)/(3sin(x) - cos(x))

Answer 1

evaluate the limit of the trigonomoteric limit

Answer 2

(0-1)/(3sin(0)-cos(0))
=-1/(3*0-1)
=-1/(0-1)
=-1/(-1)
=1

Answer 3

we cant substitute first

Answer 4

the function is continuous at x=0 so yes we can

Answer 5

:s ok i guess

Answer 6

so thats not the same as lim x-> 0 2sin (3x)/ 5x which would be equal to 6/5?

Answer 7

this function is discontinuous at x=0
we can manipulate this function though to see what happens as x->0
remember sinx/x->1 as x->0
so 3/3*2sin(3x)/5x=6/5*sin(3x)/3x=6/5*(1) since sin(3x)/3x->1 as x->0

Answer 8

ok thank you i get it

Answer 9

i forgot about continuity