How to Do Interval Notation: Example 1 Graph the interval[−2,5). Step 1: The equivalent inequality for this interval is the set ofxsatisfying−2≤x<5.xcan equal -2 because there's a square bracket next to -2, butxcan't equal 5 because there's a parenthesis next to 5. ...
Use factoring techniques to find the solution set of a polynomial inequality. Suppose you were given x^2 – x < 6. Set your right side equal to zero, as you would when solving a polynomial equation. Do this by subtracting 6 from both sides. Because this is subtraction, the inequality si...
Step 2:Set the second derivative equal to zero, and solve forx. Also, determine any values ofxfor whichf″(x)does not exist. Doing this we get x2−4x−21=0(x−7)(x+3)=0[Factor the left-hand side of the equation]x−7=0a...
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Employees who perceive their supervisors to listen well enjoy multiple benefits, including enhanced well-being. However, concerns regarding the construct validity of perceived-listening measures raise doubts about such conclusions. The perception of listening quality may reflect two factors: constructive and...
Interval notation is a simplified form of writing the solution to an inequality or system of inequalities, using the bracket and parenthesis symbols in lieu of the inequality symbols. Intervals with parentheses are called open intervals, meaning the variable cannot have the value of the endpoints. ...
How to Find Total Distance Most distance problems in calculus give you thevelocity function, which is thederivativeof theposition function.The velocity formula is normally presented as aquadratic equation. You can find total distance in two different ways: with derivatives, or byintegratingthe velocit...
Ornstein-Uhlenbeck Process:a differential equation that models the motion of a particle under friction. Punctured Disks: A flat disk with a pinprick. One example of a myriad of shapes that can be integrated in calculus, but that you won’t see in statistics. Tangent Spaces: a generalization ...