What is the sine of a 30-degree angle?The sine of a 30-degree angle is 0.5. This is derived from the properties of a 30-60-90 right triangle, where the ratio of the length of the side opposite the 30-degree angle to the hypotenuse is 1:2, resulting in a sine value of 1/2 or 0.5.
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What is the difference between a derivative and an integral?
What is the difference between a derivative and an integral?A derivative represents the rate of change of a function with respect to a variable, essentially measuring how a function changes as its input changes. An integral, on the other hand, represents the accumulation of quantities, such as areas under curves. Derivatives focus on instantaneous rates of change, while integrals focus on total accumulation.
How do you find the global maximum and minimum values of a function on a closed interval using derivatives and critical points?
How do you find the global maximum and minimum values of a function on a closed interval using derivatives and critical points?To find the global maximum and minimum values of a function on a closed interval [a, b], follow these steps: 1. Compute the derivative of the function. 2. Find the critical points by setting the derivative equal to zero and solving for x. 3. Evaluate the function at the critical points and at the endpoints a and b. 4. Compare these values to determine the global maximum and minimum.
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