# How do you find the limit of #(sin(x))/(5x)# as x approaches 0?

The limit is

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To find the limit of (sin(x))/(5x) as x approaches 0, we can use the concept of limits and trigonometric properties. By applying the limit definition, we can rewrite the expression as (sin(x))/(x) * (1/5). The limit of sin(x)/x as x approaches 0 is a well-known result and equals 1. Therefore, the limit of (sin(x))/(5x) as x approaches 0 is 1/5.

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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 of #(2x^2 + 1)^0.5 / (3x -5)# as x goes to infinity?
- For what values of x, if any, does #f(x) = e^x/(e^x-3e^x) # have vertical asymptotes?
- For what values of x, if any, does #f(x) = 1/((x^2-4)(x+1)(x-5)) # have vertical asymptotes?

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