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:
Answer: 
Step-by-step explanation:
Given : The total number of cards in a deck = 52
Number of red cards = 26
There are two types of red cards : diamond and heart.
Number of diamond cards = 13
The probability that the first card is a diamond :-
Since diamond is also a red card.
Now, the total cards left = 51
The number of red cards left = 12
The probability that the second card is a red card (without repetition) is given by :-
Now, the probability of choosing a red card for the second card drawn, if the first card, drawn without replacement, was a diamond :-
Answer:
x<1.1 or x>1.1
Step-by-step explanation:
Answer:
$0.31.
Step-by-step explanation:
If 1.10 apples cost $3.50, we should divide to find the rate per apple.
1.10/3.5 ≈ 0.31
0.31 is the aproximatley answer, since there is no clear answer (at least not from my work). 0.31*70=21.70
The cost of 70 apples are 0.31.
