# Quiz Chapter 02.03: Differentiation of Discrete Functions

 MULTIPLE CHOICE TEST NUMERICAL DIFFERENTIATION OF DISCRETE FUNCTIONS DIFFERENTIATION

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