Question

The oracle function f(x) is presented below. for each x value you enter the oracle will tell you the value f(x). calculate the derivative of the function at 0.1 using the definition?

Answer 1

To calculate the derivative of the function at 0.1 using the definition, we need to use the definition of the derivative. The derivative is the limit of the difference quotient as the change in x approaches zero.

Step-by-step explanation:

To calculate the derivative of the function at 0.1 using the definition, we need to use the definition of the derivative. The derivative is the limit of the difference quotient as the change in x approaches zero. In this case, we have:

f'(0.1) = lim(x -> 0) [f(0.1) - f(x)] / (0.1 - x)

Substituting the given function f(x) = (10 N)sin[(0.1 m-¹)x] into the above equation, we get:

f'(0.1) = lim(x -> 0) [(10 N)sin[(0.1 m-¹)(0.1)] - (10 N)sin[(0.1 m-¹)x)] / (0.1 - x)

Now, we can simplify and evaluate the limit using algebra and trigonometric identities.