F(x) = (x cosx + 3 tanx)/ (x² + sinx), For x≠0 f(x) = 4, for x=0 At x=0 is such that? (a) it is continous (b) it has irremovable discontinuity (c) it has removable discontinuity (d) lim f(x) = 3 x->0

1 Answer
Apr 28, 2018

#color(red)((c)# is correct.

Explanation:

.

#f(x)=(xcosx+3tanx)/(x^2+sinx)#

#f(x)=0/0# undefined at #x=0#

#Lim_(x->0)(xcosx+3tanx)/(x^2+sinx)=Lim_(x->0)(cosx+3sinx/x*1/cosx)/(x+sinx/x)=(1+3(1))/(0+1)=4/1=4#

This indicates that #f(x)# has a removable discontinuity at #x=0#.

Here is the graph for #-4.7 < x < 4.7#:

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Here it is for

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