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Left hand limit and right hand limit

Left-hand limit and right-hand limit: Left-hand limit: The limit of f(x) is equal to L As x approaches c from the left, That is for all x sufficiently close to …

Limit of a function concept

Limit of a function concept is divided into two part (1) descriptively (2) numerically (1) By finding the area of circumscribing regular polygon: Consider a circle of unit radius …

x approaches to infinity means

Meaning of the phrase” x approaches to infinity” Suppose a variable x assumes in succession a series of value as multiple of 10 start from 1 x approaches to infinity …

Fourth roots of unity power

Fourth roots of unity power, take variable x equal to 1 root’s power 4 this gives the 4 roots +1, -1, +ι, -ι X = ∜ 1 X= (1)¼ Suppose …

Cube root of unity power

Cube root of unity power 1, 2, 3, 4,5, 6, 7, 8, 9………………..n first we find and proof root power three of unity power 1, 2, 3, and we apply …

properties of determinant proves

Properties of determinant proves: property of determinant number 1: If the rows and columns of a determinant are changed, the value of the determinant does not change. EXAMPLE: Property …

log rule exponential of real number

Log rule exponential: If then x is called the logarithm of y to base a and written as where a >0, a ≠ 1 and y >0 That is The …

cramer’s rule pdf

Cramer’s rule PDF consider the following system of equation. a.x + b y = m………………..1 c x +d y =n…………………….2 We know that AX = B Where Ax =B can …

properties matrix

If A, B, C are m × n matrix and c and d are scalars, the following properties are true. (1) commutative property with respect to addition A+B= B+A (2) …

types of function example

Types of function example (1) Into function: If function f such that A→B is such that Range f ⊂ B that is Range f ≠ B then f is said …