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Yes. The cosine function is continuous.

The sine function is also continuous.

The tangent function, however, is not continuous.

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Yes. The cosine function is continuous.

The sine function is also continuous.

The tangent function, however, is not continuous.

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yes it is a continuous function.

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Yes, a polynomial function is always continuous

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That's true. If a function is continuous, it's (Riemman) integrable, but the converse is not true.

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Weistrass function is continuous everywhere but not differentiable everywhere

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