# How do limits work in calculus?

In Pre-Calculus, they function similarly.

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Limits in calculus are used to describe the behavior of a function as it approaches a certain value or as it approaches infinity. They are fundamental in understanding concepts such as continuity, derivatives, and integrals. A limit is defined as the value that a function approaches as the input approaches a particular value. It can be approached from both the left and right sides. Limits can be evaluated algebraically, graphically, or using various limit laws and theorems. They allow us to analyze the behavior of functions and make precise calculations in calculus.

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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.

- For what values of x, if any, does #f(x) = 1/((x-5)sin(pi+1/x) # have vertical asymptotes?
- What is # lim_(x->-oo) f(x) = sinx/(x-8)#?
- How do you find the limit of #sqrt(x^2 + 1) - x# as x approaches infinity?
- How do you find the limit of #(2x-3)/(x+5)# as #x->3#?
- How do you find the limit of #sqrt(n^2+n) - (n)# as n approaches #oo#?

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