Use the continuity to evaluate the given limit

Question

Use continuity to evaluate the limit. lim x→π cos(x + cos x)

Answer 1

f(x) = cos(x+cos(x))

To use continuity means that if f(x) is continuous.

lim x→a f(x) = f(a)

Plotting with Desmos shows that f(x) is continuous at π.

so f(π) = cos(π+cos(π))= cos(π-1) ≈ -0.54