Continuity and limts: Show a function is continuous at a f(x)=(x+2x^3)^4,

nagasenaz 2021-10-29 Answered
Continuity and limts: Show a function is continuous at a
f(x)=(x+2x3)4,a=1
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Sadie Eaton
Answered 2021-10-30 Author has 104 answers
Show a function is continuous at a
f(x)=(x+2x3)4,a=1
We have f(x)=(x+2x3)4,a=1
f(x)=(x+2x3)4 at a=-1 to be continous
if, L.H.L=R.H.L=Function at the given point
Now,
limx1f(x)=limx1(x+2x3)4=(limx1x+2(limx1x)3)4
limx1f(x)=(1+2(1)3)4=(12)4=(3)4
limx1f(x)=81
L.H.L=limx1f(x)=81
Then,
limx1f(x)=(1+2(1)3)5=(1+2)4=(3)4
R.H.L=limx1f(x)=81
Now, for f(-1)
f(1)=((1)+2(1)3)4=(12)4=(3)4
f(1)=81
Here, L.H.L=R.H.L=f(1)
Hence, f(x) is continuous at a=-1
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