Limits

Infinite limits:
Let f(x) be a function of x, if the worth of f(x) can be made greater than any pre-assigned number by taking x close to 'a', then they say
Similarly, if the worth of f (x) can be made less than any pre-assigned number by taking x close to 'a', then they say f (x) tends to - as x approaches 'a'

Introduction to indices

Indices in maths:

If m is a positive integer, a x a x a …. m times is written as am. a is called the base & m is the power. They read it as "a raised to the power m". The power is also called "the index" or "the exponent".
They know that 64 = 2 x 2 x 2 x 2 x 2 x 2 = 26
Here 2 is called the base & 6 is called the power (or index or exponent).
They say that "64 is equal to base 2 raised to the power 6".
The Laws of Indices are : 1)Product Law, 2)Quotient Law, 3)Power Law, (ab)m = am . bm.
An irrational root of a positive rational number is called a surd.

Help Variance formula

Efficiency Variance Formula :

Consider the following steps will be help to find out the efficiency variance. find expected value and the mean of the given data after that calculate the variance.
Step 1: Let take the values.
Step 2: Calculate the expected values.
Mean or expected value = sum of the values/total number of data.
Step 3: Finally find out the variance use the following efficiency variance formula.

Algebra help

Integrated algebra regents question 4:
The value of the expression −|a − b| when a = 12 and b = −3 is
(1) −15 (3) −9
(2) 15 (4) 9

Integrated algebra regents question 5:
Which expression represents in simplest form?
(1) 4x² − 2x (3) 4x² + 2x -1
(2) 4x² − 4x (4) 10x² − 4x + 1

Fraction simplification steps

Fraction simplifier:
Multiplying mixed fractions simplify fractions steps:
Here are the steps for multiply two fractions when one or both are mixed numbers:

• fraction should be changed to an improper one
• After simplifying directly multiply the numerators
• Then multiply the denominators,finally simplify the result

Factor Rules 4

Factor Rules:

Factor Rules for 4:

Factor rules for 4 mean we have to factor the number 4. Basically factor in math refers any of the number or symbols multiplied by together mean it will produce the some other number. And that multiplier and multiplicand of the factors of the resulting number. For example if we multiply 2 and 4 we will get 8. So factors of the number 8 are 2 and 4 and a number can have more than one factor.

We know a number is having more than one factors.
To find the factors of 4
the given number should be the multiplicand of 2.
We can divide the 4 = 1 x 4 = 1 x 2 x 2
So the factors of 4 is 1, 2 and 4
Here 1 is the common factor for all the number.
2 is the multiplicand of 2 so this is one of the factors of 4.
4 is the multiplicand of 2. So this is also one of the factors of 4.
We will see how to find the factors of some more numbers using the above rules.

Indefinite Integrations

Indefinite Integrations:

An indefinite integration is the family of functions that have a given function as a common derivative. The indefinite integral of f(x) is written ∫ f(x) dx.

Definite Integration:
If F(x) is the integral of function f(x) over the interval [a, b] ,i.e., ∫ f(x) dx = F(x) then the definite integral of function f(x) over the interval [a, b] is denoted by


and is defined as,





Where 'a' is called the lower limit and b is called the upper limit of integration and the interval [a, b] is called of integration.