Estimate Error: How Did He Get 4?

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In summary, the conversation was about finding the derivative and second derivative of the function f(x) = sin(2x) and determining the largest possible value for the second derivative. The participants also discussed the behavior of sin(nx) and how it affects the frequency of oscillations.
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  • #2
The function is f(x) = sin(2x). Find f'(x) and then f''(x). What is the largest possible value of f''(x)?
 
  • #3
so because sin 2x cannot be more than 1 between the pi/2 and 0??
 
  • #4
sin(x) oscillates between -1 and 1. Check on the TI.

Also, sin(nx) , such as sin(3x) , just increases the frequency I think. You can graph that too. It just squooshed the oscillations closer to the y-axis. So they are still in between -1 and 1.
 
  • #5
o ok i got it thanks
 

1. How is error estimated in scientific experiments?

In scientific experiments, error is estimated by comparing the measured value to the true value. This is typically done by calculating the difference between the two values and expressing it as a percentage or a fraction.

2. Why is it important to estimate error in scientific experiments?

Estimating error is important in scientific experiments because it allows us to determine the accuracy and reliability of our results. It also helps us to identify any sources of error and make improvements to our experimental methods.

3. How is error calculated in mathematics?

In mathematics, error is typically calculated by finding the difference between the actual value and the estimated or predicted value. This can be expressed as an absolute value or a percentage.

4. What is the difference between absolute and relative error?

Absolute error is the difference between the actual value and the estimated value, while relative error is the ratio of the absolute error to the actual value. Relative error is often used when comparing values of different magnitudes.

5. How can we reduce error in scientific experiments?

There are several ways to reduce error in scientific experiments, including increasing the sample size, improving the precision of measurements, and controlling for external variables. It is also important to carefully design and conduct the experiment to minimize potential sources of error.

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