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Mathematical Analysis
Mathematical analysis is, simply put, the study of limits and how they can be manipulated. Starting with an exhaustive study of sets, mathematical analysis then continues on to the rigorous development of calculus, differential equations, model theory, and topology. Topics including real and complex analysis, differential equations and vector calculus can be discussed in this category.
2,575 Questions
What the differentiation and anti-differentiation formula?
There is no single formula for differentiation and anti-differentiation.
The deriviative of a function y = f(x) is the limit of delta y over delta x as delta x approaches zero.
OR:
If f(x)=axn,
f'(x)=(an)xn-1
The deriviative of 2x3 would be 6x2.
The anti-deriviative of a function is the reverse operation, i.e. the function is the deriviative of the anti-deriviative.
Anti differentiation introduction:
Anti differentiation is also called as integration process. It gives the reverse value of the differentiation equation. Anti differentiation is also called as anti derivative of the function. In this anti differentiation, f(x) is anti derivative of the function F(x). Anti differentiation is used for finding the area of the region under the certain curve. Anti differentiation symbol is denoted as ∫.
General formula for anti differentiation:
∫ xn dx = [xn + 1 / (n + 1)]+ c
∫ k dx = k ∫ dx
∫ udv = uv - ∫ v du
∫ (w + y) dx = ∫ w dx + ∫ y dx
anti-differentiation
What is s in Laplace transforms?
The Laplace transform of a function f(t), defined for all real numbers t ≥ 0, is the function F(s), defined by: : The parameter s is a complex number: : with real numbers σ and ω. A complex number is defined as a number comprising a real numberpart and an imaginary number part. An imaginary number is a number in the form bi where b is a real number and i is the square root of minus one. (Wiki search)
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How many 16 x 16 patio pavers are needed to make a 12 x 12 stone patio?
81 pavers (each 16 inches square) would be needed.
12 foot x 12 foot = 144 inches x 144 inches = 20,736 in2
16 inches x 16 inches = 256 in2
20,736/256 = 81
Binomials are algebraic expressions of the sum or difference of two terms. Some binomials can be broken down into factors. One example of this is the "difference between two squares" where the binomial a2 - b2 can be factored into (a - b)(a + b)
For each age group compute the probability that a moose in that age group is killed by a wolf?
0.5 = 112
1-5= 53
6-10= 73
11-15 = 56
16-20 = 2
What are the limitations of laplace transform?
Laplace will only generate an exact answer if initial conditions are provided
Is every cauchy sequence is convergent?
Every convergent sequence is Cauchy. Every Cauchy sequence in Rk is convergent, but this is not true in general, for example within S= {x:x€R, x>0} the Cauchy sequence (1/n) has no limit in s since 0 is not a member of S.
What is a modal group in stem and leaf diagrams?
If you had a stem and leaf diagram like this for example
1/1,2,6
2/4,4,4,5,7,8,9
3/1,6
4,2
5/4,7
Key
1/1- 11 years old
The mode would be the value on the "leaf" that appears most frequently so in this case it would be 24.
However, the modal group would be the group from the "stem" that has the most values, so in this case it would focus on the 20's.
You would write it from the number on the stem to the highest in the group, like- 20-29. You would write it from 20 even if there is nobody who is actually 20 years old, as there isn't in this case.
30% Do you go to vista?
he tried to helium
What is the relationship between relative frequency and cumulative frequency?
frequency plot - number of counts relative frequency - number of counts/ total counts cumulative frequency - number of counts that are cumulatively summed cumulative relative frequency that are cumulatively summed. Examples: Let y = accidents per day for one week, and x = days of the week (1 to 7) y = (0, 0, 1, 2, 1, 5,1) for X = 1, 2, ... 7 frequency counts y = (0,0, 0.1,0.2,0.1, 0.5, 0.1) relative frequency y = (0,0,1,3,4,9,10) = cumulative frequency y = (0, 0, 0.1,0.3,0,0.4,0.9,1) cumulative relative frequency
If a function rule is 2x - 3 what is the output for 3?
Where Y = 2x-3, the output for x = 3 is Y = 3.
2x - 3 = 2(3)-3 = 6-3 = 3
What does modal class mean in mathematics?
It means that you have to find the number that you can see there more than once
Like 2,5,6,4,6,1,9
6 will be the modal class because its shown more than once
What are two prime numbers whose sum is 42?
Split the number in half and make an equation adding the two together to make the desired amount. Unless the number that is half the total is prime, adjust the first number down by an amount to make it a prime number, then adjust the second one up by an equal amount and check whether it is also a prime number. If the second number is also a prime number, you have found two prime numbers that equal the desired amount. If not, adjust the first number down to another prime number, repeating the procedure above until you have two prime numbers.
If you split 42 in half, the result is 21. Take the equation 21 + 21 = 42. Since 21 is not prime, adjust the first number down to 19 which is the first prime number below 21. That means the other number would be 23, which is prime. So, you have two prime numbers that add up to 42 = 19 + 23.
The prime factorization of 42 is 2 x 3 x 7, so it has three factors that are prime: 2, 3, and 7.
How can you find the assumed mean of grouped data?
find assumed mean data is 46,55,52,59,63,47,56,50,51,55 ,
