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The limit of a sum of functions is the sum of the limits of those functions. For example, suppose we wanted to find the limit of 2x 2 + x as x approaches 5. We simply break up the limit of the sum into the sum of the limits.
Definite integral as the limit of a Riemann sum. Definite integrals represent the exact area under a given curve, and Riemann sums are used to approximate those areas. However, if we take Riemann sums with infinite rectangles of infinitely small width (using limits), we get the exact area, i.e. the definite integral!
Limit Laws. Limit Laws are the properties of limit. They are used to calculate the limit of a function. Constant Law. The limit of a constant is the constant itself.
The limit of a difference is equal to the difference of the limits. The limit of a constant times a function is equal to the constant times the limit of the function. The limit of a product is equal to the product of the limits. The limit of a quotient is equal to the quotient of the limits.
A limit is a certain value to which a function approaches. Finding a limit usually means finding what value y is as x approaches a certain number. You would be typical phrase it as something like “the limit of a function f(x) is 7 as x approaches infinity.
The limit of a constant is the constant. For example: limb 5=5.
The definite integral is defined to be exactly the limit and summation that we looked at in the last section to find the net area between a function and the x -axis. Collectively we'll often call a and b the interval of integration.
The number a that is at the bottom of the integral sign is called the lower limit of the integral and the number b at the top of the integral sign is called the upper limit of the integral.
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