# How do you find #lim (1-cosx)/x# as #x->0# using l'Hospital's Rule?

Therefore:

Hopefully this helps!

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To find lim (1-cosx)/x as x approaches 0 using L'Hospital's Rule, you first need to check if the limit is in an indeterminate form, which it is (0/0). Then, you can differentiate the numerator and the denominator separately with respect to x. After differentiation, you can evaluate the limit again. Here's the process:

Given lim (1-cosx)/x as x approaches 0:

- Differentiate the numerator: d(1-cosx)/dx = sin(x)
- Differentiate the denominator: dx/dx = 1
- Rewrite the limit with the derivatives: lim sin(x)/1 as x approaches 0
- Evaluate the limit: sin(0)/1 = 0

Therefore, lim (1-cosx)/x as x approaches 0 is equal to 0.

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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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