Quiz Chapter 02.03: Differentiation of Discrete Functions


(All Tests)


(More on Discrete Differentiation)


(More on Differentiation)

Pick the most appropriate answer

1. The definition of the first derivative of a function f \left( x \right) is


2. Using forward divided difference with a step size of 0.2, the derivative of the function at x=2 is given as

x 1.8 2.0 2.2 2.4 2.6
f \left( x \right) 6.0496 7.3890 9.0250 11.023 13.464

3. A student finds the numerical value of {f}' \left( x \right) = 20.219 at x=3 using a step size of 0.2. Which of the following methods did the student use to conduct the differentiation if it is given in the table below?

x 2.6 2.8 3.0 3.2 3.4 3.6
f \left( x \right) e^{2.6} e^{2.8} e^{3} e^{3.2} e^{3.4} e^{3.6}

4. The upward velocity is given as a function in the table below.

t \left( s \right) 10 15 20 22
v \left( m/s \right) 22 36 57 10

To find the acceleration at t=17 \, s, a scientist finds a second order polynomial approximation for velocity, and then differentiates it to find the acceleration. The estimate of the acceleration at t=17 s in m/s2 most nearly is


5. The velocity of the rocket is given as a function of time in the table below.

t \left( s \right) 0 0.5 1.2 1.5 1.8
v \left( m/s \right) 0 213 223 275 300

Allowed to use forward, backward, or central divided difference approximation of the first derivative, your best estimate for the acceleration  a=\dfrac{dv}{dt} of the rocket in m/s2 at t=1.5 seconds is


6. In a circuit with an inductor of inductance L, a resistor with resistance R, and a variable voltage source E \left( t \right), where E \left( t \right) = L \dfrac{di}{dt} + Ri, the current, i, is measured at several values of time as

Time t \left( s \right) 1.00 1.01 1.03 1.1
Current, i (amperes) 3.10 3.12 3.18 3.24

If L=0.98 Henries and R=0.142 ohms, your choice for most accurate answer for E \left( 1.00 \right) would be