without using a grpahing calc and table of values
2007-10-01 09:50:00 · 3 answers · asked by maximumheat_89 1 in Science & Mathematics ➔ Mathematics
ok..but how did u get from stpe 1 to step 2..why are you multiplying by 3/5
2007-10-01 10:01:34 · update #1
lim (x -> 0) tan3x/tan5x
= lim(x -> 0) [tan3x/(3x)] / [tan5x/(5x)] * (3/5)
= 3/5
[ because as x->0, 3x->0 and 5x->0, so lim(3x->0) tan3x/(3x) = 1 and lim(5x->0) tan5x/(5x) = 1]
2007-10-01 09:57:24 · answer #1 · answered by Madhukar 7 · 0⤊ 1⤋
lim x --> 0 tan3x/tan5x = 0/0 is indetreminate so use L'Hospital/s rule
lim x --> 0 = 3sec^2x/(5sec^2x) = 3/5 = .6
2007-10-01 10:00:26 · answer #2 · answered by ironduke8159 7 · 0⤊ 0⤋
tanx = sinx/cosx
sin 3x/cos 3x / sin5x multiply and divide by 3x and 5x
the likely expressions you should get are
sin5x/5x and it's recipoical and cos 3x/3x and it's reciprocal you know those limits don't you
2007-10-01 09:58:37 · answer #3 · answered by Anonymous · 0⤊ 1⤋