Is Rolle's theorem applicable to #f(x)=tanx#, when 0 < x < r??
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Yes, Rolle's theorem is applicable to ( f(x) = \tan(x) ) on the interval ( 0 < x < r ), where ( r ) is any positive real number. Since ( \tan(x) ) is continuous and differentiable on the interval ( 0 < x < r ), and ( \tan(x) ) is continuous on the closed interval ( 0 \leq x \leq r ), and differentiable on the open interval ( 0 < x < r ), all the conditions required by Rolle's theorem are satisfied. Therefore, there exists at least one ( c ) in the open interval ( 0 < c < r ) such that ( f'(c) = 0 ).
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No, Rolle's theorem is not applicable to ( f(x) = \tan(x) ) on the interval ( 0 < x < r ), where ( r ) is any positive real number.
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When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
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