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Show that the function f (x) = |sin x + cos x| is continuous at x = p. Examine the differentiability of f, where f is defined by
Show that the function f (x) = |sin x + cos x| is continuous at x = p. Examine the differentiability of f, where f is defined by
CBSE | Class 12 | Continuity and Differentiability | Exercise 1 | Maths | NCERT Exemplar
Show that the function f (x) = |sin x + cos x| is continuous at x = p. Examine the differentiability of f, where f is defined by

Given,

\[f\left( x \right)\text{ }=\text{ }\left| sin\text{ }x\text{ }+\text{ }cos\text{ }x \right|\text{ }at\text{ }x\text{ }=\text{ }\pi \]

Presently, put \[g\left( x \right)\text{ }=\text{ }sin\text{ }x\text{ }+\text{ }cos\text{ }x\text{ }and\text{ }h\left( x \right)\text{ }=\text{ }\left| x \right|\]

Thus, \[h\left[ g\left( x \right) \right]\text{ }=\text{ }h\left( sin\text{ }x\text{ }+\text{ }cos\text{ }x \right)\text{ }=\text{ }\left| sin\text{ }x\text{ }+\text{ }cos\text{ }x \right|\]

Presently,

\[g\left( x \right)\text{ }=\text{ }sin\text{ }x\text{ }+\text{ }cos\text{ }x\] is a nonstop capacity since wrongdoing x and cos x are two persistent capacities at \[x\text{ }=\text{ }\pi .\]

We realize that, each modulus work is a typical capacity is a nonstop capacity all over the place.

Thusly, \[f\left( x \right)\text{ }=\text{ }\left| sin\text{ }x\text{ }+\text{ }cos\text{ }x \right|\] is consistent capacity at \[x\text{ }=\text{ }\pi .\]

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