Question

F(x)=|sinx+cosx|....show its continuous at x=π

Answer 1

Step-by-step explanation:

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!!!

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