Answer:
The integral symbol in the previous definition should look familiar. We have seen similar notation in the chapter on Applications of Derivatives, where we used the indefinite integral symbol (without the a and b above and below) to represent an antiderivative. Although the notation for indefinite integrals may look similar to the notation for a definite integral, they are not the same. A definite integral is a number. An indefinite integral is a family of functions. Later in this chapter we examine how these concepts are related. However, close attention should always be paid to notation so we know whether we’re working with a definite integral or an indefinite integral.
Integral notation goes back to the late seventeenth century and is one of the contributions of Gottfried Wilhelm Leibniz, who is often considered to be the codiscoverer of calculus, along with Isaac Newton. The integration symbol ∫ is an elongated S, suggesting sigma or summation. On a definite integral, above and below the summation symbol are the boundaries of the interval, \left[a,b\right]. The numbers a and b are x-values and are called the limits of integration; specifically, a is the lower limit and b is the upper limit. To clarify, we are using the word limit in two different ways in the context of the definite integral. First, we talk about the limit of a sum as n\to \infty . Second, the boundaries of the region are called the limits of integration.
We call the function f(x) the integrand, and the dx indicates that f(x) is a function with respect to x, called the variable of integration. Note that, like the index in a sum, the variable of integration is a dummy variable, and has no impact on the computation of the integral.
his leads to the following theorem, which we state without proof.
Step-by-step explanation:
The amount that you should be willing to rent an additional oven when the order size is 1 dozen cookies is the amount that is less than the profit of producing those cookies.
<h3 /><h3>What amount should be paid to rent an additional oven?</h3>
The dozen cookies that Kristen’s Cookie Company are about to make are an additional order which means that they do not have the ovens to make it.
They will therefore have to rent an additional oven. If they did this, the amount they pay for the additional oven should not give them losses. They should therefore rent the oven at a cost that is less than the profit they will get for the additional 1 dozen cookies.
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Answer:
He spent $825 at the store.
Step-by-step explanation:
4/44=11 11x75=825
ax - x = c Factor out the x
x (a - 1) = c Divide both sides by (a - 1)
x = 
