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Let a and b be fixed real numbers such that a < b on a number line. The different types of intervals we have are
The open interval (a, b): We define an open interval (a, b) with end points a and b as a set of all real numbers "x", such that a < x < b. That is, the real number x will be taking all the values between a and b. An important point to consider in this case is the type of brackets used. Generally open intervals are denoted by ordinary brackets ( ). The closed interval [a, b]: We define a closed interval [a, b] with end points a and b as a set of all real numbers "x", such that a ≤ x ≤ b. In this case the real number x will be taking all the values between a and b inclusive of the end points a and b. Generally closed intervals are denoted by [ ] brackets. The half open interval [a, b): We define a half open interval [a, b) with end points a and b as a set of all real numbers "x", such that a ≤ x < b. In this case the real number x will be taking all the values between a and b, inclusive of only a but not b. The half open interval (a, b]: We define a half open interval (a, b] with end points a and b as a set of all real numbers "x", such that a < x ≤ b. In this case the real number x will be taking all the values between a and b, inclusive of only b but not a.
The open interval (a, b): We define an open interval (a, b) with end points a and b as a set of all real numbers "x", such that a < x < b. That is, the real number x will be taking all the values between a and b. An important point to consider in this case is the type of brackets used. Generally open intervals are denoted by ordinary brackets ( ).
The closed interval [a, b]: We define a closed interval [a, b] with end points a and b as a set of all real numbers "x", such that a ≤ x ≤ b. In this case the real number x will be taking all the values between a and b inclusive of the end points a and b. Generally closed intervals are denoted by [ ] brackets.
The half open interval [a, b): We define a half open interval [a, b) with end points a and b as a set of all real numbers "x", such that a ≤ x < b. In this case the real number x will be taking all the values between a and b, inclusive of only a but not b.
The half open interval (a, b]: We define a half open interval (a, b] with end points a and b as a set of all real numbers "x", such that a < x ≤ b. In this case the real number x will be taking all the values between a and b, inclusive of only b but not a.
Evaluate following limits. (a) (b) Solution There in fact isn't a whole lot to this limit. In this case because there is only a 6 in the denominator we'l
Bayes’ Theorem In its general form, Bayes' theorem deals with specific events, such as A 1 , A 2 ,...., A k , that have prior probabilities. These events are mutually exclusive
if 500kg of food lasts 40 days for 30 men.how many men will consume 675kg of food in 45 days.
Sketch the phase portrait for the given system. Solution : From the last illustration we know that the eigenvectors and eigenvalues for this system are, This tu
Surface Area- Applications of integrals In this part we are going to look again at solids of revolution. We very firstly looked at them back in Calculus I while we found the
what is a sample space diagram
The low temperature in Anchorage, Alaska present was -4°F. The low temperature in Los Angeles, California was 63°F. What is the difference in the two low temperatures? Visualiz
It is the simplest case which we can consider. Unforced or free vibrations sense that F(t) = 0 and undamped vibrations implies that g = 0. Under this case the differential equation
Q1: Find three positive numbers whose sum is 54 and whose product is as large as possible.
Let's start things by searching for a mixing problem. Previously we saw these were back in the first order section. In those problems we had a tank of liquid with several kinds of
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