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Show that thefunction f (x) = | sin x + ...

Show that thefunction` f (x) = | sin x + cos x |` is continuous at `x =pi`

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We have

`f(x)=|sin x+cos x| at x=pi`

Use `g(x)=sin x+cos x and h(x)=|x|`

` therefore h[g(x)]=h(sin x+cos x)=|sin x+cos x|`

after that `, g(x)=sin x+cos x` is a continuous function so sin x and cos x are two continuous functions at `x=pi.`

every modulus function is a continuous function everywhere.

so , `f(x)=|sin x+cos x|` is continuous function at `x=pi.`
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