Questions asked by Sarah.

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• Compute Δy and dy for x = 16 and dx = Δx = 1. (Round the answers to three decimal places.)? y = √x
  
• Use Newton's method with the specified initial approximation x1 to find x3, the third approximation to the root of the given equation. (Round your answer to four decimal places.) What is x3?
  
• Use Newton's method to approximate the given number correct to eight decimal places?
  
• Use Newton's method to approximate the indicated root of the equation correct to six decimal places?
  
• Use Newton's method to find all roots of the equation correct to six decimal places?
  
• Find the root of the equation. Give your answers correct to six decimal places?
  
• Use Newton's method to find the coordinates of the inflection point of the curve?
  
• Consider a particle moving along the x-axis where x(t) is the position of the particle at time t A particle, initially at rest, moves along the x-axis such that its acceleration at time t > 0 is given by a(t)=5cos(t). At t=0, its position is x=2?
  
• A model rocket is fired vertically upward from rest. Its acceleration for the first 3 seconds is a(t) = 60t at which time the fuel is exhausted and it becomes a freely "falling" body. 14 seconds later, the rocket's parachute opens, and the (down)?
  
• A stone was dropped off a cliff and hit the ground with a speed of 104 ft/s. What is the height of the cliff? (Use 32 ft/s2 for the acceleration due to gravity.)?
  
• A car is traveling at 50 mi/h when the brakes are fully applied, producing a constant deceleration of 32 ft/s2. What is the distance covered before the car comes to a stop? (Round your answer to one decimal place.)?
  
• How to find the definite integral using the limit definition?
  
• How to balance the following redox problems using both methods?