check the discontinuity of f(x)={2x+3 x≤2 ,2 x-3 x-2 x>2 }
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Step-by-step explanation:
lim(x–>2-) f(x)..................here(x–>2-) indicate x<2
=lim(x–>2-) (2x+3)
= (2*2 +3)
=7
lim(x–>2) f(x)..................here(x–>2) indicate x=2
=lim(x–>2-) (2x+3)
= (2*2 +3)
=7
lim(x–>2+) f(x)...................here(x–>2+) indicate x>2
=lim(x–>2+) 2(x-3)(x-2)
= 2(2-3)(2-2)
=0
lim(x–>2-) f(x) =lim(x–>2) f(x) not =lim(x–>2+) f(x)
so, this indicate the discontinuity.
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