Limit as X approaches 4

[sin(6x)]/x

Question

Limit as X approaches 4

[sin(6x)]/x

amistre64 · Answer

sin(u) = u - u^3/3! +  u^5/5! - u^7/7! + ...

sin(6x) = 6x - (6x)^3/3! +  (6x)^5/5! - (6x)^7/7! + ...

sin(6x)/x = 6 - 6^2 x/3! +  6^5 x^4/5! - 6^7 x^6/7! + ...

hmmm

amistre64 · Answer

seems to me to be simpler to just plug in x=4 since there is no divide by 0 from it

anonymous · Answer

Ia m sorry, i wrote it wrong, it is x approaching 0

anonymous · Answer

My bad.

amistre64 · Answer

oh, then the power series is useful since its a polynomial; all the x terms zero out and we are left with the first term

amistre64 · Answer

does [ ]  indicate something like a step function, or is that just your way of seperating the top from the bottom?

anonymous · Answer

its just my way to separate it

amistre64 · Answer

k, then since:

sin(6x)/x = 6 - 6^2 x/3! +  6^5 x^4/5! - 6^7 x^6/7! + ...

when x=0 we have

sin(6(0))/0 = 6 - 0 + 0 - 0 + 0 - 0 + 0 - .... = 6

anonymous · Answer

since it is all divided by zero, wouldn't the answer be zero?

anonymous · Answer

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