# Given #sin x/ x^2# how do you find the limit as x approaches 0?

You should use the fact that

You can modify the expression as follows:

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To find the limit as x approaches 0 for sin(x)/x^2, we can use L'Hôpital's Rule. By applying this rule, we differentiate both the numerator and denominator separately with respect to x.

The derivative of sin(x) is cos(x), and the derivative of x^2 is 2x.

Taking the limit as x approaches 0, we have:

lim(x→0) sin(x)/x^2 = lim(x→0) cos(x)/2x

Now, we can evaluate this new limit. By substituting x = 0 into the expression, we get an indeterminate form of 0/0.

To resolve this, we can again apply L'Hôpital's Rule. Differentiating the numerator and denominator once more, we have:

lim(x→0) cos(x)/2x = lim(x→0) -sin(x)/2

Now, substituting x = 0 into the expression, we get -sin(0)/2 = 0/2 = 0.

Therefore, the limit as x approaches 0 for sin(x)/x^2 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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- How do you find the limit of #(4x^2 -3x+2)/(7x^2 +2x-1)# as x approaches infinity?

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