Evaluate the Limit, as x approaches 0, of (tg(x) - sin(x))/(x - sin(x))

[huba4buba]

Here is the difficult one
Initially I tried to solve it using l'hopital's rule, but it turns to be 0/0

lim x approaches 0, (tg(x) - sin(x))/(x - sin(x))


Does anybody can solve it ?

 

[Deleted member 4993]

Here is the difficult one
Initially I tried to solve it using l'hopital's rule, but it turns to be 0/0

lim x approaches 0, (tg(x) - sin(x))/(x - sin(x))


Does anybody can solve it ?

Apply L'Hospital's rule again and again......

 

[lookagain]

Here is the difficult one
Initially I tried to solve it using l'hopital's rule, but it turns to be 0/0

lim x approaches 0, (tg(x) - sin(x))/(x - sin(x))


Does anybody can solve it ?

\(\displaystyle \displaystyle\lim_{x \to 0} \dfrac{tan(x) \ - \ sin(x)}{x \ - \ sin(x)}\)


My suggestion is to apply L'Hopital's Rule a total of two times and convert every
trig function to sine or cosine, depending. Then divide every term in the "larger
numerator" and the "larger denominator" by sin(x).

Finally, evaluate the limit of the resultant trigonometric expression.

 

[huba4buba]

Apply L'Hospital's rule again and again......

\(\displaystyle \displaystyle\lim_{x \to 0} \dfrac{tan(x) \ - \ sin(x)}{x \ - \ sin(x)}\)


My suggestion is to apply L'Hopital's Rule a total of two times and convert every
trig function to sine or cosine, depending. Then divide every term in the "larger
numerator" and the "larger denominator" by sin(x).

Finally, evaluate the limit of the resultant trigonometric expression.

Thank you very much !