What exactly is a limit in calculus?

Answer 1
A limit allows us to examine the tendency of a function around a given point even when the function is not defined at the point. Let us look at the function below. #f(x)={x^2-1}/{x-1}# Since its denominator is zero when #x=1#, #f(1)# is undefined; however, its limit at #x=1# exists and indicates that the function value approaches #2# there. #lim_{x to 1}{x^2-1}/{x-1} =lim_{x to 1}{(x+1)(x-1)}/{x-1} =lim_{x to 1}(x+1)=2#

This tool is very helpful in calculus when the definition of the derivative is motivated by the fact that the slopes of secant lines with approaching intersection points approximate the slope of a tangent line.

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Answer 2

In calculus, a limit is a fundamental concept that describes the behavior of a function as its input approaches a certain value. It represents the value that a function approaches as the input gets arbitrarily close to a particular point. Limits are used to analyze the behavior of functions, determine continuity, and evaluate derivatives and integrals.

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Answer from HIX Tutor

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.

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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