Let \(P\left(x_{0}, f\left(x_{0}\right)\right)\) be a fixed point on the graph of the differential function f with a domain that is the set of real numbers.

a. Determine the real number \(z_{0}\) such that point \(Q\left(x_{0}+1, z_{0}\right)\) is situated on the line tangent to the graph of f at point P.

b. Determine the unit vector u with initial point P and terminal point Q.

Text Transcription:

P(x_0, f(x_0))

z_0

Q(x_0 + 1, z_0)

Exam 3 Study Guide Momentum, Rotational Motion, Torque Momentum moves in the same direction as velocity and is given by the equation: p=mv The initial momentum is always the same as the final momentum. In the problems that ask for recoil motion use the following formula often times in momentum problems they are paired with translational kinematic equations: m1v 1m v2 2 An open systems is a system that gains or loses mass. This is the formula to us for the rocket or a similar system: ∆ M F thrust ∆t ) The angular position is given in polar coordinates and is found with the following: s θ= r Angular displacement is the change in angular position and is given by the following: ∆ θ=θ fθ i The average angular speed is shown by: θ −θ ∆θ ω av f = tf−ti ∆t Angular Acceleration is given in the following equation: a= ω fω i= ∆ω tf−ti ∆t Similar to translational kinematic equations there are rotational kinematic equations. For these velocity is replaced by ω and x is replaced by θ. These act the same way as translational kinematic equations. To find tangential velocity use: