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step1536
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Given points (0.8,0.5), (1.2,1.5)
f(x) =x^2 |x^2-1| < 1/2 whenever |x-1| <delta correct to four decimals round down if necessary
You have shown an attempt at a solution, but haven't shown the problem itself. This makes it more difficult for us to determine what you're trying to do. Please add this information. Punctuation would be nice, too.step1536 said:Given points (0.8,0.5), (1.2,1.5)
f(x) =x^2 |x^2-1| < 1/2 whenever |x-1| <delta correct to four decimals round down if necessary
The precise definition of a limit is the mathematical concept that describes the behavior of a function as its input approaches a certain value. It is the value that a function approaches as its input gets closer and closer to a specific value, but may never actually reach that value.
The limit of a function is calculated by evaluating the function at values that are closer and closer to the desired value, and observing the behavior of the function at those values. This can be done algebraically, graphically, or using numerical methods.
If a function has no limit, it means that the function either approaches different values from the left and right sides of the desired value, or that the function approaches infinity or negative infinity as the input approaches the desired value. In this case, the limit does not exist.
The concept of a limit is important in mathematics because it allows us to understand the behavior of functions and their values at specific points. It is also a fundamental concept in calculus and is used to define other important concepts such as derivatives and integrals.
The concept of a limit is used in many practical applications, such as in physics, engineering, and economics. It is used to analyze rates of change, optimize functions, and make predictions. For example, the concept of a limit is used in physics to calculate instantaneous velocity and acceleration, and in economics to model supply and demand curves.