Examine continuity of the function `f(x) = x^(3) + 2x^(2)- 1` at `x = 1`.

Answer

N/a

Explanation

We have, `f(x) = x^(3) + 2x^(2)- 1` at `x = 1`.
`:. underset(xrarr1^(+))(lim)f(x) = underset(hrarr0)(lim)(1+h)^(3)+2(1+h)^(2)-1 = 2`
and `underset(xrarr1^(-))(lim)f(x)=underset(hrarr0)(lim)(1-h)^(3)+2(1-h)^(2)-1=2`
`:. underset(xrarr1^(+))lim=underset(xrarr1^(-))limf(x)`
and `f(1) = 1+2-1=2`
So, `f(x)` is continuous at `x = 1`