# How do you find the limit of #(cos x)^(1/x^2)# as x approaches 0?

This is still indeterminate so you must apply L'Hopital's Rule again.

You can now get the limit by substitution.

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To find the limit of (cos x)^(1/x^2) as x approaches 0, we can use the properties of limits and the natural logarithm. Taking the natural logarithm of the expression, we get ln((cos x)^(1/x^2)). By applying the logarithmic property, this simplifies to (1/x^2) * ln(cos x).

Now, we can evaluate the limit of this expression as x approaches 0. As x approaches 0, ln(cos x) approaches ln(cos 0) = ln(1) = 0.

Therefore, the limit of (cos x)^(1/x^2) as x approaches 0 is equal to e^0, which is equal to 1.

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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.

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- What is the limit as x approaches 0 of #sin(4x)/tan(5x)#?
- How do you evaluate the limit of #-x^4+x^3-2x+1# as #x->-1#?

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