Exponential function: Any function represented as f(x)= is called exponential function, where a>0 and a .
Domain of an exponential function is R, set of all real numbers and range is (0, ) because exponential function attains only positive values.
For more on exponential and logarithmic functions, visit here…https://celestialtutors.com/topic/exponential-and-logarithmic-functions/
Polar coordinate system is a plane with Pole(point O) and polar axis which is horizontal axis from point O. Any point P in this plane is assigned polar coordinates represented as P(r, theta)
we measure theta as positive when moving counterclockwise and negative when moving clockwise.
If r > 0, then P is on the terminal side of theta . If r < 0, then P is on the terminal side of (theta + pi).
A complex number is represented as a+ib where a is real part and b is imaginary part. The complex number a+ib can also be represented as ordered pair(a,b) and plotted as a point in Argand plane. In this plane horizontal axis is called real axis and vertical axis is called imaginary axis.
An algebraic expression containing two terms is called binomial expression. The general form of the binomial expression is (x+a) and the expansion of (x+a)^n, where n is a natural number, is called binomial theorem. It gives a formula for the expansion of the powers of binomial expression.
The coefficients in the binomial expansion follow a specific pattern known as Pascal’s triangle.
Following are some important features of Pascal’s triangle.
-Each row is bounded by 1 on both sides.
-Any entry except first and last, is the sum of two entries in preceding row , one on the immediate left and other on immediate right.
Some important conclusions from the Binomial Theorem:
Total number of terms in binomial expansion is n+1.
The coefficients of terms equidistant from the beginning and end are equal. These coefficients are known as binomial coefficients.
The terms in the expansion of (x-a)^n are alternatively positive and negative first being positive always.
The coefficient of x^r in (r+1)th term in the expansion of (x+a)^n is (_r^n)C.
For more help on this topic, please visit..https://celestialtutors.com/topic/pascals-triangle-and-binomial-theorem-2/
The word equation is derived from word ‘equal’. Any expression having equal (=) sign is called equation. If any linear algebraic expression in one variable is equal to some integer or some other algebraic expression, then it is called algebraic equation.
Linear equations can be categorized as follows
1. When variable is only one side.
2. When variable is on both sides
When variable is only on one side: We always solve the equation for an unknown variable using the same operations on both sides so that equation doesn’t become uneven and both sides remain balanced.
When variable is on both sides:
When variables on both sides of equation, we try to bring the variables together either on left or on right side and then move forward with the same process of isolating variable
For detailed explanation on this topic , please reach at…https://celestialtutors.com/topic/how-to-solve-linear-equation-in-one-variable/
I’m delighted to present this website to help the students all over the world. This website help students with their homework assignments and test preparations through two channels – Live help and Assignment help. This site encourage and motivate students for conceptual understanding of topics.
I welcome all students to the new session. Lets start this session with all enthusiasm and positivity. It is said that well begun is half done. Try not to skip the initial classes as they set out equation right with our mentors, classmates and of course with math itself! You must have a solid foundation if you are going to have a strong superstructure. So build your basic math concepts strong to sail throughout the session , successfully with flying colors. Enjoy learning and enjoy Math !
I wish all of you have a successful academic session and bright future ahead!!