# How do you determine the limit of #sin(x)/x# as x approaches infinity?

Or, all the limits are equal.

So, recall that

Then,

So,

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To determine the limit of sin(x)/x as x approaches infinity, we can use the concept of L'Hôpital's Rule. By applying this rule, we differentiate both the numerator and denominator with respect to x. The derivative of sin(x) is cos(x), and the derivative of x is 1.

Taking the limit of the derivative of sin(x) divided by the derivative of x as x approaches infinity, we get the limit of cos(x)/1. Since the cosine function oscillates between -1 and 1, there is no definite limit for cos(x) as x approaches infinity. Therefore, the limit of sin(x)/x as x approaches infinity is undefined.

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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.

- How do you find the limit of # (tan2x)/(5x)# as x approaches 0?
- How do you find the limit of #2sin(x-1)# as x approaches 0?
- How do you find the limit of #(2x+1)^4/(3x^2+1)^2# as #x->oo#?
- How do you find the limit of #(sqrt(x+6)-x)/(x^3-3x^2)# as #x->-oo#?
- What is the limit of #(3x^2+20x)/(4x^2+9)# as x goes to infinity?

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