# Using Newton's Method to Approximate Solutions to Equations - Page 3

Questions

- Solve the equation #e^x = 3-2x#?
- How do we find our approximation for #2.9^5#?
- How do you use Newton's Method to approximate #root5(20) # ?
- A differentiable function has the property that f(5) = 4 and f'(5) = 3. What is the estimate for f(4.8) using the local linear approximation for f at x=5?
- A pendulum of length L feet has a period of: #T= 3.14(L^.5)/2(2^.5)# seconds. If you increase the length of a 1-foot pendulum by .01 feet, how much does its period increase?
- How do you use linear approximation about x=100 to estimate #1/sqrt(99.8)#?
- If point of inflection of #y=e^(-x^2)# is at #y=1/e^a#, #a=..........#?
- How do you find the linear approximation of #f(x)=ln x# at x=1 and use it to estimate ln 1.42?
- What is the local linearization of #e^sin(x)# near x=1?
- How do you use a linear approximation or differentials to estimate #1/1002#?
- Find the root of the equation. Give your answers correct to six decimal places?
- How do you estimate the quantity using the Linear Approximation and find the error using a calculator #(15.8)^(1/4)#?
- How to prove newton's method?
- How do you use Newton's method to find the approximate solution to the equation #x^4=x+1,x<0#?
- How do you find the linear approximation L to f at the designated point P. compare the error in approximating f by L at the specified point Q with the distance between P and Q given #f(x,y) = 1/sqrt(x^2+y^2)#, P(4,3) and Q(3.92, 3.01)?
- How do you estimate the quantity using the Linear Approximation of #(3.9)^(1/2)#?
- How do you estimate the quantity using Linear Approximation and find the error using a calculator of #1/(sqrt(95)) - 1/(sqrt(98))#?
- How do you use linear approximation to the square root function to estimate square roots #sqrt 4.400#?
- How do you use the linear approximation to #f(x, y)=(5x^2)/(y^2+12)# at (4 ,10) to estimate f(4.1, 9.8)?
- How do you use Newton's method to find the approximate solution to the equation #x^4=x+1,x>0#?