Holistic Numerical Methods Institute

committed to bringing numerical methods to undergraduates

Multiple Choice Test

Discrete Functions

 

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

x

1.8

2.0

2.2

2.4

2.6

f(x)

6.0496

7.3890

9.0250

11.023

13.464

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?

x

2.6

2.8

3.0

3.2

3.4

3.6

f(x)

e2.6

e2.8

e3.2

 

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.

 

t

 s

10

15

20

22

v

22

36

57

10

 

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.

 

t (s)

0

0.5

1.2

1.5

1.8

v (m/s)

0

213

223

275

300

 

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

 

Time, t (s)

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(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

 

 

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