Limited Trigonometry - III

Calculus Level 5

f(x)=tan(x2)sec(x)+tan(x22)sec(x2)++tan(x2n)sec(x2n1)f(x)=\tan\left( \frac{x}{2} \right) \cdot \sec \left( x \right)+\tan\left( \frac{x}{2^2} \right) \cdot \sec \left( \frac{x}{2} \right)+\ldots+\tan\left( \frac{x}{2^n} \right) \cdot \sec \left( \frac{x}{2^{n-1}} \right) g(x)=f(x)+tan(x2n) g(x)=f(x)+\tan\left( \frac{x}{2^n} \right)

where x(π2,π2)x \in \left( -\frac{\pi}{2} , \frac{\pi}{2} \right) and nNn \in \mathbb{N}

Evaluate the limit : limx0(g(x)x)1x3 \displaystyle \lim_{x \to 0} \left( \dfrac{g(x)}{x} \right)^{\frac{1}{x^3}}


Join the Brilliant Classes and enjoy the excellence.
×

Problem Loading...

Note Loading...

Set Loading...