Question

in a sum involving limits fr ex : $\lim_{x \to \0}0$ a + cos x
here if we take the constat term out , we will get 1+ cos x or only cos x please answr if you really know it

Answer 1

Heya!!

Lt ( a + Cos x )

x--->0

If we take constant term out we get

a × Lt ( 1 + {Cos x }/a )

x--->0

Answer 2

You cannot take out 'a' simply out. Cauz limit is common for both terms in a + cosx

So correct way to proceed will be to distribute limit to both terms in the equation as showm below.

$\lim_{x \to \0}o (a+ cosx) = \lim_{x\to \0}o (a) + \lim_{x\to \0}o (cosx)\\ = 0 + cos (0)\\\\=1$