Is the function defined by `f(x)=x^2-sinx+5`continuous at `x=pi`?

Explanation

`f(x) = x^(2) - sin x + 5 `
at x = `pi`
`f(pi) = pi^(2)- sin pi + 5 = pi^(2) + 5 `
L.H.L `underset(x to pi^(-))(lim)f(x)`
Let `pi - h = x `
`rArr pi + h to pi`
`rArr h to 0 `
`underset(h to 0)(lim)f(pi - h)`
`underset(h to 0)(lim)(pi - h)^(2)- sin ( pi- h)+ 5`
`underset(h to 0)(lim)(pi - h)^(2)- sin ( pi- h)+ 5`
`underset(h to 0)(lim)(pi - h)^(2)- sin h + 5`
`(pi - 0 ) ^(2) - sin 0 + 5 pi^(2) + 5 `
R.H.L. `underset(x to pi^(+))(lim)f(x)`
`underset(h to 0)(lim)f(pi + h)`
`underset(h to 0)(lim)(pi + h)^(2)- sin ( pi+ h)+ 5`
`underset(h to 0)(lim)(pi + h)^(2) + sin h + 5`
`(pi + 0) ^(2) + sin 0 + 5 pi^(2) + 5 `
`:'` L.H.L. `f(pi)` R.H.L.
`:.` f(x) is contnuous at x = ` pi` .