Question

Show that the function f(x) = |sin x + cos x| is continuous at x = π .

Answer 1

Hey there!!!

we have,  f(x) = |sin x + cos x| at x = π
Let , g(x) = sin x + cos x
and, h(x) = |x|
therefore, hog(x) = h [g(x)]
                             = h (sin x + cos x)
                             = | sin x + cos x|

Since, g(x) = sin x + cos x is a continuous function as it is forming with addition to two continuous functions , sin x and cos x.
Also, h(x) = |x|  is also a continuous function. Since we know that composite functions of two continuous functions is also a continuous function.
Hence, f(x) = |sin x + cos x| is a continuous function everywhere.

so, f(x) is continuous at x = π

HOPE IT HELPS YOU!!!
# RUHANIKA...

Answer 2

Hi______
the given function is |sinx+cosx|
for proof continous we to satisfy 3 condition of continuous .
but here we not need it
because
we know that
since sinx and cosx functions are continuously everywhere
so we know that linear combinations of continuous functions is again continuous function.
we also know that the modulus of continuous function is again continuous function .
Another way you can see it is by observing that:
see in image
hope it help