Asked by Jin
how do you find sin7x/4x when lim x goes to 0
the answer is 7/4
the answer is 7/4
Answers
Answered by
drwls
One way would be to write sin 7x in infinite series form, and divide out 4x.
sin7x= 7x - (1/3!)(7x)^3 + (1/5!)(7x)^5 - ...
After dividing by 4x, the only term that does not vanish as x->0 is 7/4.
You could also use L'Hopital's rule. Take the ratio of the x-derivatives of the numerator and denominator.
sin7x= 7x - (1/3!)(7x)^3 + (1/5!)(7x)^5 - ...
After dividing by 4x, the only term that does not vanish as x->0 is 7/4.
You could also use L'Hopital's rule. Take the ratio of the x-derivatives of the numerator and denominator.
Answered by
Tutorteddy
Using L'Hospital rule
Lim sin7x/4x as x ->0 = Lim sim7x/Lim 4x as x->0 = Sin (Lim 7x)/(Lim 4x)as x-> 0 = 7/4 (on differentiating both numerator and denominator w.r.t. x) = 7/4
Lim sin7x/4x as x ->0 = Lim sim7x/Lim 4x as x->0 = Sin (Lim 7x)/(Lim 4x)as x-> 0 = 7/4 (on differentiating both numerator and denominator w.r.t. x) = 7/4
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