I understand what it really is from reading and learning about it. I understand it is the slope of a given function. How do you prove that this limit is actually the slope of the function? Is the slope defined using this limit or if it is something else then ow to prove that the limit is actually the slope of the function.
Thanks in advance!
I want to know when maths actually becomes something that is not entering value in a formula and solve for an unknown but something that requires attention and basis of understanding. I think calculus is where maths becomes something that requires understanding and is not completely formula based.
Lets say on quadratic equation has roots i and -i so he equation will be x^2+1=0 Now let say that another quadratic equation has roots 2i and i then the quadratic will be x^2 -3ix -2=0. Now in this case the roots of the equation x^2+1 and x^2 -3ix-2 have one root in common . But they say it is impossible
I am talking about this one A_n = i^(n) + j^(n) (works with minus sign also) then the recursive equation (if the quadratic equation whose roots ae i and j is ax^(2) +bx +c=) is a(A_(n+2) +b_(n+1) +c_n=0 can this formula be extended?
I am learning differentiation and when I was learning differentiation of inverse trigonometric functions it involved substitution of x (the input of the inverse trigonometric function) as sintheta or tantheta . I understood all of this well but when I was learning all of this the book never noted about the triangular inequality. Like should not we first verify if the term we are dealing with is conformable with the triangular inequality before doing anything related to triangles? Basically my doubt is shouldnt we first verify if the term we are dealing with satisfies the triangular inequality before we do trigonometric substitution because i9f we do not do that then our substitution will be wrong since the terms we are dealing with can never form a triangle and hence can never have trigonometry. Atleast if we are not proving that the terms satisfy the triangular inequality shouldnt we atleast change the domain of the function such that the given input will satisfy the triangular inequality.
Thanks in advance!
PS: Even though I have not learnt integration yet I have seen videos where people solve integrals using trigonometric substitution but they bring in the triangle and never talk about the triangular inequality
I am learning Gauss law in physics and there I was introduced to Gaussian surface. Is any closed 3-D shape a Gaussian surface or are there any other specifications?
Thanks in advance!
Let us say i have two functions f(x) and g(x). In general their domains are not equal but over an interval their range and values are equal at every point so can we say that these fuctions are identical over an interval.
Thanks in advance!
I recently did an experiment on Voltaic cells (variation in current and Voltage by changing the distance between electrodes) right now I have some values for this experiment. I understand that I can just use existing formula from the internet and then show that my values match approximately the theoretical values. But I want to derive a formula using my values as the sole input and try to reach something that is close to the actual formula. My first try was to plot a graph and try to reach a straight line graph by plotting various types of the graph and then using the equation of a straight line reach the actual formula but I am not sure if I will get a correct graph with my values (they are certainly not very accurate) so what should I do?
Also please suggest some videos on plotting graphs on a graphing calculator using our own values and getting a corresponding function that matches our graph.
Thanks in advance!
f(x)={x}=x-[x] using this definition of the function I get {-1.7} 0.3. But if I take the meaning of the name of the function {1.3}=1+3/10 hence 3/10 or 0.3 is the fractional part. But if we want to use this on negative numbers {-1.7} I get -1 - 7/10 hence -7/10 is the fractional part right ?
Thanks in advance!
x+y+z=5
2x+2y+2z=7
3x+3y+3z=6
I tried forming the determinants but each of them evaluate to 0. This implies there are infinite solutions whereas the answer is no solution
I understood by geometry that these planes are parallel to each other hence inconsistent but why doesnt this fact reflect in determinants?
Thanks in advance!
All these derivations involve considering an element then integrating. But I am not able to consider an element to start my derivation on. I am not able to do these derivations even after looking at them for multiple times it just seems very hard. I am not very good at integration can this be a reason?
Thanks in advance!
I only learnt these theorems but never understood the proof (I but then I understood the proof of factor theorem from remainder theorem) I tried searching on did not understand it. Can someone please explain it?
Thanks in advance!
Before calculus was there , there was practically no need to develop logarithms (of course useful for calculations) but before people discovered the properties of logarithms that enable this calculations. What was the need of logarithms? Was it created just like how imaginary numbers were created (to solve equations) or did mathematicians create it to analyze the exponents?
In the sense that after some point I wont understand what the topic is about and I will not be able to solve questions?