![\displaystyle \int \sqrt[4]{\tan x}dx](/latexrender/pictures/dc8f98b38a94c51f80a1c94db7fc222b.png "\displaystyle \int \sqrt[4]{\tan x}dx")
and 
. Then 
be a polynomial of degree 
such that 
for 
for which the equation 
has one real solution
, Then 
Using Geometry.
and 
are three vectors such that
and 
and 
for real 
.Then find Range of 
and for real .Then find Range of 
and 
are angle of a 
. Then 
![\lim_{x\rightarrow0} \frac{\sqrt[]{x+2}-\sqrt[]{2}}{x} = \lim_{x\rightarrow \0}\frac{\left(\sqrt{x+2}-\sqrt{2}\right)}{x}.\frac{\left(\sqrt{x+2}+\sqrt{2}\right)}{\left(\sqrt{x+2}+\sqrt{2}\right)} = \frac{1}{2\sqrt{2}}](/latexrender/pictures/80f4f9d32c740f7aa3ce47772953282c.png "\lim_{x\rightarrow0} \frac{\sqrt[]{x+2}-\sqrt[]{2}}{x} = \lim_{x\rightarrow \0}\frac{\left(\sqrt{x+2}-\sqrt{2}\right)}{x}.\frac{\left(\sqrt{x+2}+\sqrt{2}\right)}{\left(\sqrt{x+2}+\sqrt{2}\right)} = \frac{1}{2\sqrt{2}}")
![\lim_{x\rightarrow-\infty}\frac{\sqrt[]{x^2+4}}{x+4}](/latexrender/pictures/8751ce32f529536fa70cffb806d7890a.png "\lim_{x\rightarrow-\infty}\frac{\sqrt[]{x^2+4}}{x+4}")
