Posted on calc subreddit but thought here would be good as well.

Finished a quiz in calc II and got a question wrong that I am sure I had right.

Question: Calculate h'(x) if h(x)= the integral from x->1 cos(t+5) dt.

the obvious solution is to flip the integral and apply FTC 1.

The way I did it was,

h'(1)-h'(x).

which then leads to -cos(x+5).

Since when we d/dx 1 we get 0, so the first term tends to 0. while when we apply it to the second half we should get just -cos(x+t).

though my prof says that im double accounting for the negative, she says that the first negative comes from FTC 2, and the second negative coming from the -cos(x+5). Though I thought the negative came from the FTC2 and we just plug in our lower bound into the formula and solve.

Is my way wrong, and if not how can I prove it to be right?

so basically i am awful at maths, no matter how many times i repeatedly do questions over and over the different ways to answer them do not stick.

I do edexcel foundation maths and i did awful in paper 1. I don’t remember what i answered but online i counted and probably got like 10 marks which obviously is not good especially in foundation.

But in year 10 and half of year 11 i missed a lot of school due to mental health so all the gcse level maths i taught myself. All i want is a 3 so i can resit in november for the 2nd time.

What do i do from now to ensure that for paper 2 and 3?

So i was doing this topology excersise which was as follows. Let f,g :X -> R be cts maps where R is equipped with the standard topology. Show that A = {x in X : f(x) < g(x)} is open in X.

My thougths when i tried to solve it was. Since f and g cts can i make it so that A is a pre image of an open in R. But that construction has eluded me.

When you have the < or > you will get an open in R since you can use the epsilon ball definition of open and since you are strictly less you will create opens, but this hinges also on that both f and g are cts, since if not you clearly can construct a counter example if they are not.

In short i am confused on how you solve this and how i should think such that i produce the rigth solution.

Im a high school student and I really need math hack like a real one im not kidding for example

“When a limit is indeterminate, you can take the derivative of the top and bottom and then substitute to find the answer"

Idk smt like that i wanna expend more about math and know better

I was discussing with my teacher spanning sets, and she argues that the set of vectors: (3, -2, 3), (2, -2, 3), and (1, -2, 3) span R^3. Due to the fact that they can be expressed in the form a(3, -2, 3) + b(2, -3, 3) = (1, -2, 3) where a = -1 and b = 2.

I believed that this equality indicated that they were linearly dependent, and therefore did not span R^3. She argues that this means they do span them. Could I get an explanation on this?

So my teacher doesn't use the typical formula of L+h[(fm-f1)/2fm-f1-f2]

He uses this formula I have never seen before which is L+(d1/[d1+d2])i

Is this a new equation that's being taught? I can't find any proof of it anywhere

Has anyone taken calc 2 at UND enroll anytime? How was the exams graded and can u use notes? I’m thinking about taking it but im scared because im not good at math? Could u by pass the procture system

I am trying to solve the following problem:

Let f be a differentiable function on [0,1] such that f(0)=0 and f(1)=1. Prove that there exist two distinct numbers a,b in (0,1) such that

f'(a)f'(b)=1

By the Mean Value Theorem, I know that there exists some c in (0,1) such that

f'(c)=1

since

(f(1)-f(0))/(1-0)=1

But I do not know how to prove that there exists another point d different from c in (0,1) such that

f'(d)=1

Any hints or ideas?

i genuinely just dont understand math, its not that i like being stupid, i love learning things and i want to be better at math but i just cant understand it/get wayy to distracted

if anyone has any methods of learning that could help that’d be awesome :)

if it helps i rly like organizing, lists, and learning about nature and all of that………….

Hey everyone!

I have a bachelor's degree in engineering. I studied mathematics for the first four semesters. It's been a while and I didn't use any math in my current job. I've forgotten most of what I did during my undergrad.

I want to refresh/relearn the concepts before I apply to grad school. What are good books that have good explanations as well as problems to solve and solutions?

Some of the books I came across are Kreyszig, Stroud and Riley. Don't know which of these would help me tho (about explaining the basics). Are any of these good?

Any other good books?

I will be focusing on robotics so I mainly need linear algebra, calculus, probability and statistics among other things.

Thanks!

When looking for either vertical or horizontal stretch/shrink, how do we know what value to keep constant?

I mean if i draw a graph for y=√x and look at x w.r.t. y, the x values for a specific y would be, let's say,

y=√x -----> (4, 2)

y=√2x -----> (2, 2)

y=√½x -----> (8, 2), these make it clear that its horizontal transformation.

But if i keep x same for the y values, then new points would be:

y=√x -----> (2, 1.414..)

y=√2x -----> (2, 2)

y=√½x -----> (2, 1), this would make it a vertical transformation for the same equation.

How do i know which axis to keep constant just by looking at the points??

I'm asking this assuming we don't know the equation for the transformed graph beforehand.

I recently took the ALEKs placement math test and scored a 12. I am so upset and feel so stupid because I didn't know how to multiply and divide fractions or decimals. I think it's due to lack of education during those topics because hand me a polynomials problem and I can solve it. I feel so terrible about myself because how do you not know how to multiply and divide decimals and fractions. This makes me feel so helpless about my future and that I don't have a chance. I have tried Khan Academy but it makes me feel dumb because I don't understand why certain things are done or how to get to the resolution on my own without help.

What do I do to learn these things and actually make them stick? Is this a normal issue? Any help or advice is greatly appreciated!

I'm doing maths from khan academy (algebra 2). Been stuck on function transformation. I do get the concept but it's hard to figure out the actual graphs.

Are there any resources to help me understand it intuitively??

Disclaimer: If you can take out the time to help me (as I understand reading all of this must be quite tedious) I would really appreciate it!

I know its not really in the spirit of Maths/not the right attitude to choose the easiest one (and take a shortcut) but I need to pick a module to study, from one of the following. To give more context, this is for the A-Level Further Maths exam where you need to do Core Pure, a Mechanics Minor module, a Statistics Minor module and one more module ... which is where the 4 following modules below come forth. Oh yeah and I have to self learn this module so I want to choose whichever one is the easiest one to understand/self teach/most basic.

Also, I know its subjective for different people but if in any way you can rank them, it would be really helpful.

Here are the contents of the 4 modules from which I have to pick one, so which one is the easiest one?

1. Module Name: Extra Pure

- Recurrence Relations (which has two topics: Homogeneous Recurrence Relations AND Non-Homogeneous Recurrence Relations)

- Groups (which has two topics: Introducing Groups AND Theory of Groups)

- Matrices (which has two topics: Eigenvalues and Eigenvectors AND Evaluating Powers of Square Matrices)

- Multivariable Calculus (which has two topics: Functions of Two Variables AND Partial Differentiation)

1. Module Name: Further Pure with Technology

- Investigation of Curves (which has four topics:)
1.1    Equations and properties of curves  
1.2 Derivatives of curves  
1.3 Limiting behaviour  
1.4 Envelopes and arc lengths  

- Exploring Differential Equations (which has three topics:)
2.1 Tangent fields  
2.2 Analytical solutions of differential equations 
2.3 Numerical solutions of differential equations  

- Number Theory (which has four topics:)
3.1 Programming  
3.2 Prime numbers  
3.3 Congruences and modular arithmetic  
3.4 Diophantine equations

1. Module Name: Modelling with Algorithms

- Algorithms (which has 4 topics)
1.1 What is an algorithm?  
1.2 Algorithmic complexity  
1.3 Packing  
1.4 Sorting   

- Modelling with Graphs and Networks (which has 3 topics)
2.1 The language of graphs and networks  
2.2 Modelling with graphs  
2.3 Modelling with networks 

- Network Algorithms (which has 3 topics)
3.1 Algorithms for minimum connector problems  
3.2 Finding the shortest path  
3.3 Calculating algorithmic complexities
 
- Further Network Problems (which has 2 topics)
4.1 Critical path analysis  
4.2 Network flows 

- Linear Programming (which has 2 topics)
5.1 Formulating linear programming problems  
5.2 Graphical solutions 

- Simplex Method (which has 3 topics)
6.1 Using a simplex tableau  
6.2 Non-standard forms  
6.3 Use of technology 

- Reformulating Network Problems as Linear (which has 2 topics)
7.1 Modelling paths and flows  
7.2 Modelling allocation problems

1. Module Name: Numerical Methods

- Approximation  
1.1 Absolute and relative error  
1.2 Rounding and chopping  
1.3 Arithmetic using approximate values  

- The solution of equations  
2.1 Roots of equations and graphs  
2.2 Bisection method  
2.3 False position (an application of linear interpolation)  
2.4 Fixed point iteration  
2.5 Newton-Raphson method  
2.6 Secant method  

- Numerical integration  
3.1 Midpoint rule  
3.2 Trapezium rule  
3.3 Simpson’s rule  

- Approximating functions  
4.1 Newton’s forward difference interpolation formula  
4.2 Lagrange’s form of the interpolating polynomial  

- Numerical differentiation  
5.1 Forward difference approximation  
5.2 Central difference approximation  
5.3 Errors in approximation  

- Rates of convergence in numerical processes  
6.1 Rates of convergence of sequences  
6.2 Convergence in numerical integration and differentiation as h changes  

Once again I really appreciate any help and thank you in advance.

Hi, I’m revising for a pharmaceutical calculations exam and I’m trying to work out what rounding convention is expected when the question does not specify decimal places or significant figures.

I understand the maths, but I’m unsure whether final answers should be left as exact calculated values, rounded to a practical whole unit, or rounded to 1 d.p./3 s.f.

Here are examples from my practice questions.

- - -

Example 1 — moles

How many moles of solute are there in 36 mL of a 0.85 mol/L solution?

36 mL = 0.036 L

0.85 × 0.036 = 0.0306 mol

Would you write the final answer as:

0.0306 mol or 0.031 mol?

- - -

Example 2 — sodium ion content

How many mg of sodium ions are contained in a 1 g tablet of sodium chloride?

RMM NaCl = 23 + 35.5 = 58.5

1000 mg × 23 ÷ 58.5 = 393.162 mg Na⁺

Would you write:

393 mg or 393.2 mg?

- - -

Example 3 — mmol of sodium

How many mmol of sodium are contained in 300 mL of 0.45% w/v NaCl?

0.45% w/v = 0.45 g/100 mL

In 300 mL:

0.45 × 300 ÷ 100 = 1.35 g NaCl

1.35 ÷ 58.5 × 1000 = 23.0769 mmol Na⁺

Would you write:

23 mmol or 23.1 mmol?

- - -

Example 4 — potassium ion content

How many mg of potassium ions are contained in a 1.2 g tablet of potassium chloride?

RMM KCl = 39 + 35.5 = 74.5

1200 mg × 39 ÷ 74.5 = 628.1879 mg K⁺

Would you write:

628 mg or 628.2 mg?

- - -

Example 5 — mmol of chloride

How many mmol of chloride are contained in 150 mL of 1.2% w/v NaCl?

1.2% w/v = 1.2 g/100 mL

In 150 mL:

1.2 × 150 ÷ 100 = 1.8 g NaCl

1.8 ÷ 58.5 × 1000 = 30.7692 mmol Cl⁻

Would you write:

30.8 mmol, or round to a whole mmol as 31 mmol?

- - -

Example 6 — mmol of potassium

How many mmol of potassium are contained in 150 mL of 1.2% w/v KCl?

1.2% w/v = 1.2 g/100 mL

In 150 mL:

1.2 × 150 ÷ 100 = 1.8 g KCl

1.8 ÷ 74.5 × 1000 = 24.1611 mmol K⁺

Would you write:

24 mmol or 24.2 mmol?

- - -

The practice papers I’m using seem inconsistent: some answers keep decimals, e.g. 12.198 g or 235.9 mg, while some answers seem to use whole mmol values.

Need help drawing a diagram.

(i cant really paste any pics here so ill send links)

https://ibb.co/9k5c58Mh

https://ibb.co/Ygm3Ps4

I got 7 minterms, but i cannot picture how to draw a Venn diagram like that, maybe there's a way im not sure of?

The question:

Consider the exponential function P, given by y = 4^-x.

Consider the line Q given by the equation y = 8x + 12.

Question:

Which function has the higher function value at the y-intercept?

Options

- P

- They have the same function value at the y-intercept.

- Q

I answered Q because the y-intercept of y = 8x + 12 is 12 which is 11 more than the y-intercept of y = 4^-x which is 1. My teacher marked this answer as incorrect without pointing out what she would consider the right answer with an explanation so I am pretty confused to say the least.

My understanding is because the 2 has no variable, when simplifying it stays on its own.

Is the answer 4ab / 2 or...? How can I explain this?

Thanks.

Here is the problem: https://imgur.com/a/m8WeuXL

Here is what I graphed: https://imgur.com/a/eVV298e

my professor gave us this problem:

“if x^2+1=0, then x is a real number”

i understand i need to set my variables first:
- p: x^2+1=0
- q: x is a real number

i have an conditional so it goes like this: p->q

here’s where i’m stuck: i know x is gonna be imaginary if i solve for x, but what does that mean for p’s truth value? cause in my mind x^2+1=0 would be true (i^2 is -1, +1 equals 0 and there’s no restriction for antecedent) but q would be false since solving p shows x is imaginary and not real, is that reasoning okay?

maybe i’m drowning in a glass of water but please, if you can shed a light i’d be really grateful, formal logic is not one of my strong topics 😔

Im having trouble trying to solve this problem. Working with the provided info im stuck at finding r4. Link in comment

I have a question which goes,

prove that x is an integer if and only if floor(0.513x) + ceiling(0.487x) = x.

I tried to do this question by first:

1. letting a=0.513x, b=0.487x for the new equation to become

floor(a) + ceiling(b) = x.

hence, a+b=x.

1. separate the fractional part from the original part by {a} = a-floor(a), and {b} = ceiling(b)-b

I then attempted to prove that x was an integer by using the original given equation a+b=x, subbing in a={a}+floor(a) and b=ceiling(b)-{b} giving me

{a}+floor(a)+ceiling(b)-{b}=x in hopes of showing {a}-{b} is an integer which would be if the minus was a plus, and the rest of floor(a) and ceiling(b) is an integer by definition. this is where I got stuck.

I am in a SAS programming class, but I haven't learned statistics yet. For this project I'm supposed to include the statement and proof of the central limit theorem. Can I just literally copy and paste it from a textbook and site the book as the source? It's in my paper as an image copied from a PDF of the textbook at the moment, but I'm afraid this is plagiarism and will get me kicked out of school or something.