Is the function f(x) = x^3 + 2x^2 – 5 cos x + 3 continuous at x = π/2 ? Justify.

Question

Is the function f(x) = x³ + 2x² – 5 cos x + 3 continuous at x = \(\frac{\pi}{2}?\) Justify.

Answer 1

Given, f(x) = x³ + 2x² – 5 cos x + 3

\(\therefore\) p(x) is a polynomial function

\(\therefore\) It is continuous at each value of x and q(x) = 5 cos x

Here, 5 is constant function and cos x is cosine function which is continuous.

\(\therefore\) q(x) is continuous at each value of x

\(\therefore\) f(x) is a difference of two continuous function which is always continuous

\(\therefore\) f(x) is continuous at x \(=\frac{\pi}{2}\)