Is this formula continous on the interval (-1,1)
h(theta)=(theta)sin(theta)
How do you enter theta into the calculator to graph the function. Also, am I suppose to plug in the numbers into the function to determine if it is continous
Theta will be in radians. Put your calculator in rad mode.
You need to get your calculator book on how to graph functions...
To determine if the given formula, h(theta) = theta * sin(theta), is continuous on the interval (-1, 1), we need to check two conditions:
1. The function is defined for all values of theta in the interval (-1, 1).
2. The limit of the function as theta approaches any value within the interval (-1, 1) exists.
To graph the function on a calculator, you need to follow these steps:
1. Turn on your calculator and open the graphing feature.
2. Enter the formula h(theta) = theta * sin(theta) into the calculator. Most graphing calculators have a store or "y=" function to define the equation.
3. Input the formula using the appropriate syntax for your calculator. Usually, the theta symbol is represented by "x" on calculators, so you should enter h(x) = x * sin(x).
4. Set the viewing window by adjusting the x-axis range to include the interval (-1, 1). You can usually find the window settings in the "Window" or "Zoom" options on the calculator.
5. Graph the function by selecting the appropriate option, such as "Graph" or "Draw."
To determine continuity, you do not need to plug in specific numbers. Instead, you need to check the two conditions mentioned earlier. We'll go through each condition:
1. The function is defined for all values of theta in the interval (-1, 1):
Since sin(theta) is defined for all real numbers, and multiplying it by theta will not affect the domain, h(theta) = theta * sin(theta) is defined for all values of theta in (-1, 1).
2. The limit of the function as theta approaches any value within the interval (-1, 1) exists:
To check this condition, you can evaluate the limit as theta approaches a specific value, such as -1 or 1, using algebraic manipulation or numerical approximation methods. If the limit exists and is equal to the value of the function at that point, then the function is continuous at that point. Repeat this process for various values within the interval to verify the continuity.
In summary, to determine if the function h(theta) = theta * sin(theta) is continuous on the interval (-1, 1):
1. Graph the function on a calculator by entering h(x) = x * sin(x).
2. Verify that the function is defined for all values of theta in (-1, 1).
3. Check the limits as theta approaches various values within the interval to determine if they exist and match the function's value at those points.