How do you evaluate the limit of #lim_(x->0)(1+x+2^x-cosx)#?

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Answer 1 · 2018-06-18T19:21:23

#lim_(x->0)(1+x+2^x-cosx)=1#

We use the property of limits to evaluate it:

#lim_(x->c)(f(x)+g(x))=lim_(x->c)f(x)+lim_(x->c)g(x)#

So

#lim_(x->0)(1+x+2^x-cosx)=#

#=lim_(x->0)1+lim_(x->0)x+lim_(x->0)2^x-lim_(x->0)cosx#

#=1+0+1-1#

#=1#