Question

Use difference quotients with delta x=0.1 and delta y=0.1 to:

a) Find the derivative
b) Approximate a definite integral
c) Evaluate a limit
d) Estimate a function value

Answer 1

To find the derivative, approximate a definite integral, evaluate a limit, and estimate a function value using difference quotients with given values of delta x and delta y.

Step-by-step explanation:

To find the derivative using difference quotients, we can use the formula:

dy/dx = (f(x + delta x) - f(x))/delta x

Using the given values of delta x = 0.1 and delta y = 0.1, we can substitute them into the formula to find the derivative.

For approximating a definite integral, we can use the formula:

Integral(f(x)) = delta x * (f(x1) + f(x2) + ... + f(xn-1) + f(xn))

Again, substituting the given values into the formula will give us an approximation of the definite integral.

For evaluating a limit, we can use the concept of difference quotients to approach the limit as delta x tends to 0.

Finally, for estimating a function value, we can use the formula:

f(x) = f(a) + (x - a) * f'(a)

Substituting the values of x and a into the formula will give us an estimation of the function value.