Applications of Derivatives 2

This is a formative assessment to see how well you have understood the content from the first 3 weeks of the course. It will not count towards your final mark. If you get less than 40%, then you should take immediate steps to improve your knowledge, such as attending Study Clinics.

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ENG1003: Digital tutorial, Week 3, Semester 2

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Practice questions for the toroidal solenoid.

Tutorial questions focusing upon the Coulomb field, electrostatic potentials and parallel plate capacitors

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Maths 1 B week 1 to week 6 content

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Given a quantity per day, how many per week

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Week 2, Question 2

Week 2, Question 1

multiple choice question on this week's content

This is the question for week 9 of the MA100 course at the LSE. It looks at material from chapters 17 and 18.

Description of variables for part b:
For part b we want to have four functions such that the derivative of one of them, evaluated at 0, gives 0; but for the rest we do not get 0. We also want two of the ones that do not give 0, to be such that the derivative of their sum, evaluated at 0, gives 0; but when we do this for any other sum of two of our functions, we do not get 0. Ultimately this part of the question will show that even if two functions are not in a vector space (the space of functions with derivate equal to 0 when evaluated at 0), then their sum could nonetheless be in that vector space. We want variables which statisfy:

a,b,c,d,f,g,h,j,k,l,m,n are variables satisfying

Function 1: x^2 + ax + b sin(cx)
Function 2: x^2 + dx + f sin(gx)
Function 3: x^2 + hx + j sin(kx)
Function 4: x^2 + lx + m sin(nx)

u,v,w,r are variables satifying
u=a+bc
v=d+fg
w=h+jk
r=l+mn

The derivatives of each function, evaluated at zero, are:
Function 1: u
Function 2: v
Function 3: w
Function 4: r

So we will define
u as random(-5..5 except(0))
v as -u
w as 0
r as random(-5..5 except(0) except(u) except(-u))

Then the derivative of function 3, evaluated at 0, gives 0. The other functions give non-zero.
Also, the derivative of function 1 + function 2 gives 0. The other combinations of two functions give nonzero.

We now take b,c,f,g,j,k,m,n to be defined as \random(-3..3 except(0)).
We then define a,d,h,l to satisfy
u=a+bc
v=d+fg
w=h+jk
r=l+mn

Description for variables of part e:

Please look at the description of each variable for part e in the variables section, first.
As described, the vectors V3_1 , V3_2 , V3_3 are linearly independent. We will simply write v1 , v2 , v3 here.
In part e we ask the student to determine which of the following sets span, are linearly independent, are both, are neither:

both: v1,v2,v3
span: v1,v1+v2,v1+v2+v3, v1+v2+v3,2*v1+v2+v3
lin ind: v1+v2+v3
neither: v2+v3 , 2*v2 + 2*v3
neither:v1+v3,v1-2*v3,2*v1-v3
neither: v1+v2,v1-v2,v1-2*v2,2*v1-v2

Introductory exercises about set theory designed to prepare students for their first lectures on the subject.

Introductory exercises about set theory designed to prepare students for their first lectures on the subject.

Formative assessment to introduce the concepts of modular arithmetic.

Introductory exercises about set theory designed to prepare students for their first lectures on the subject.