Linearization

The linearization of function y=f(x) near the value x=a is given by:

f(x)= cos x , $$a=\frac{\pi}{2}$$ , approximate cos 1.75 without calculator

approximate $$\sqrt[]{1.02}$$ without calculator

Use linearization to approximate $$\sqrt[]{123}$$

Use Linearization to approximate $$\sqrt[3]{26}$$

Let L(x) = 3(x - 4) - 2.  Find L(3.9).

y=x⁵ +37x, x=1 , dx=0.001

y=sin 3x , x=Pi , dx=-0.02

Let y = x³

Find the differential when x =2 and dx = 0.1.

Find dy if dy/dx = 7 and dx = 1/2. 

Explain the concept of Newton's method to approximate zeros of a function.

What is the formula to update the guess in Newton's method?

Use Newton's Method to solve x³ +3x+1=0 , x₀ = -0.3

Use Newton's method to solve x³ +4x² -x-1=0 , x₀=-1

When does Newton's method fail to find an approximate zero of a function?