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Question
Is the function defined by f(x) = x2 − sin x + 5 continuous at x = π?
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Solution
f(x) = x2 − sin (x) + 5
If f(x) is continuous at x = π, it implies:
f(π) = `lim_(x -> pi^+)` f(x) = `lim _(x -> pi^-)` f(x)
⇒ (π2 − sin (π) + 5) = (π2 − sin (π) + 5) = (π2 − sin (π) + 5)
⇒ π2 + 5 = π2 + 5 = π2 + 5
Which is true, i.e., f(x) is continuous at x = π.
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