Q1. The definition of the first derivative of a function f(x) is

Q2.  Using forward divided difference with a step size of 0.2, the derivative of the function at x=2 is given as

6.697
7.389

7.438
8.179

Q3. A student finds the numerical value of  f ' (x)=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 is given in the table below?

Backward Divided Difference

Calculus, that is, exact
Central Divided Difference

Forward Divided Difference

Q4. The upward velocity of a body is given as a function of time in the table below.

To find the acceleration at t=17s, 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=17s in m/s² most nearly is

4.060

4.200

8.157
8.498

Q5. The velocity of the rocket is given as a function of time in the table below.

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

83.33
128.33

173.33

183.33

Q6. In a circuit with an inductor of inductance L, a resistor with resistance R, and a variable voltage source E(t),

The current, i, is measured at several values of time as

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

0.98*(3.24-3.10)/0.1+(0.142)(3.10)

0.142*3.10

0.98*(3.12-3.10)/0.01+(0.142)(3.10)

0.98*(3.12-3.10)/0.01

Complete Solution

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