# What is the limit as x approaches 0 of #(tan^2x)/(3x)#?

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The limit as x approaches 0 of (tan^2x)/(3x) is 1/3.

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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.

- What is the value of #lim_(x-> 0) (1/3 + x)/x - (1/3 - x)/x#?
- How do you evaluate the limit #(sqrt(x+19)-3)/(x+10)# as x approaches #-10#?
- How do you find the limit of #ln(sinx)# as #x->0^-#?
- Find the limit as x approaches infinity of #y=(1.001)^x#?
- What are the removable and non-removable discontinuities, if any, of #f(x)=(2x^2+4x-70)/(x-5)#?

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