Linear Approximation/Differentials/mean Value Theorem

Question 1

If these problems require a calculator..

Answer 1

I have made a mistake

Question 2

What is the formula for linear Approximation?

Answer 2

f(x_0+(delta x)=f(x_0)+f”(x_0)(delta x)

Question 3

Differentials

Answer 3

dy=f’(x)dx, so dy/dx=f’(x)

Question 4

Differentials

Answer 4

delta y= dy, find change in y and substitute appropriately into derivative

Question 5

Mean Value Theorem-If — is — on the closed interval [a,b] and differentiable on the open interval (a,b), then there is at least one point “c” in (a, b) such that

Answer 5

f, continuous, (f(b)-f(a))/(b-a)=f’(c)