Types of Lines

Types of Lines:In this blog let us learn about types of Lines,these three are the most important types of lines in math.Parallel line,Perpendicular line, and Intersecting line.Now that we have understood about types of lines we will learn about product rule.

Fundamental Theorem of Calculus

Fundamental Theorem of Calculus:The fundamental theorem of calculus 1 handled the differentiation, integration and inverse operations are process here now.Significant of Fundamental Theorem of Calculus 1:-Let [f(x)] is a continuous function on the closed interval [[a, b]] .Let the area function [ A(x)] be defined by [A(x) = int_a^xf(x)dx for xgt=a].Then [A'(x) = f(x)] for all [x in [a,b]].Let [f(x)] be a continuous function defined on an interval [[a,b].].If [ intf(x)dx = F(x)] then [ int_a^a f(x)dx = F(x)]^b_a =F(b) - F (a) ] is called the definite integral or [f (x) ] among the limits [a] and [b].This declaration is also known as fundamental theorem of calculus 1.We identify [b] the upper limit of [x] and [a] the lower limit.If in place of [F(x)] we take [F(x) +c ] as the value of the integral, we have:[= [F (b) + c] - [F (a) + c]]

[= F (b) + c - F (a) - c]

[= F (b) - F (a)] .

Fifth Grade Math

--> Fifth Grade Math:Let us see one example of fifth grade math,we can solve one problem here, 1. Find the value of s in the given expression if t = 10. s= t
Solution
Given t = 10
The equation is s = t
s = t + 12
Substitute the value of t
s= 10+12
s = 22.Let us now learn the definition of an acute angle,acute definition- The acute angle is the type of angle which measures the angle between 0 to 90 degree and less than the 90 degree. I hope the above explanation was useful.

Regular Polygon

Regular Polygon:A polygon is a 2-dimensional object; it is a plane shape with straight sides.Commonly A Regular Polygon has included the following two conditions: All sides are equal, and all angles are equal.Examples for regular polygons: Like that triangles, squares (quadrilateral), pentagons, hexagons and so on.The area of polygon measures the size of the region enclosed by the polygon. This is usually expressed in terms of some square unit.The area regular polygon is equal to the number of triangles formed by the radii times their height.Hope you like the above example of Regular Polygon.

Area of a Circle

Area of a circle:Introduction to area of a circle:Area is the measure of surface occupied by an object. The standard unit for measurement of area is metres quare (m2).However the area of smaller dimensions can be expressed in mm2 or cm2. The areas of large dimensions can be expressed in acre or hectare.We can find the area of a circle by using the formula as, A=πr2.Here r is the radius of a circle.It is easy to find the area of a circle by applying the formula given above.Hope you like the above example of Area of a circle.Please leave your comments, if you have any doubts.

Algebra equation

Algebra equation solver:Let us understand what we mean by the concept of algebraic equation.Every algebraic equation of degree n ≥ 1 has a root real or complex.An algebraic equation solver is a statement where two algebraic expressions are equal.We can understand this concept better with the help of an Algebra equations examples.
Some Problems:

1) Sum of a number and three is 5

Solution: x+3 = 5 where x is the number

Vertical Tangent

Vertical Tangent:

In geometry, the tangent line (or simply the tangent) to a curve at a given point is the straight line that "just touches" the curve at that point (in the sense explained more precisely below). As it passes through the point where the tangent line and the curve meet, or the point of tangency, the tangent line is "going in the same direction" as the curve, and in this sense it is the best straight-line approximation to the curve at that point.


In mathematics, a vertical tangent is tangent line to be vertical. Since a vertical line contain infinite slope, a function whose graph contain a vertical tangent be not differentiable on the point of tangency. During the definition of the slope, vertical lines are excluded. Although from a simply geometric point of view, a curve might contain a vertical tangent. Imagine of a circle (with two vertical tangent lines). We still contain an equation, namely x=c, except it be not of the form y = ax+b.In fact, such tangent lines contain an infinite slope.
Limit Definition of Vertical Tangent

A function ƒ have a vertical tangent on x = a. Condition the difference quotient use to identify the derivative have infinite limit:

[lim_(h->0)(f(a+h)-f(a))/(h)=+oo] (or [lim_(h->0)(f(a+h)-f(a))/(h)=-oo]

The first case corresponds toward an upward-sloping vertical tangent, with the second case toward a downward-sloping vertical tangent. Easily speaking, the graph of ƒ have a vertical tangent at x = a condition the derivative of ƒ on a be either positive or negative infinity.



Used for a continuous function, it is often possible toward detect a vertical tangent through taking the limit of the derivative.

if [lim_(x->a)f'(x)=+oo]

After that ƒ have to contain an upward-sloping vertical tangent at x = a. In the same way, if

if [lim_(x->a)f'(x)=-oo]

then ƒ have to contain an downward-sloping vertical tangent at x = a. Within these situations, the vertical tangent toward ƒ appears since a vertical asymptote on the graph of the derivative.Let us now look at few examples of Vertical Tangents.

Examples of Vertical Tangent

Example 1 for vertical tangent

The function

[f(x) = root(4)(x)]

have a vertical tangent at x = 0, while it is continuous also

[lim_(x->0)f'(x)=lim_(x->0)(1)/root(4)(x^2)=oo]

[g(x)=root(4)(x^2)]

Have a vertical cusp on x = 0, given that it be continuous,

[lim_(x->0)g'(x)=lim_(x->0)(1)/root(4)(x)=+oo]

[lim_(x->0^-)g'(x)=lim_(x->0^-)(1)/root(4)(x)=-oo]

Example 2 for vertical tangent

What value of x does the function (you mean the graph of the equation) 5x^2+2xy+y^2=36 have a vertical tangent line?

Solution

5x^2 + 2xy + y^2 = 36
and put y = -x
5x^2 - 2x^2 + x^2 = 36
4x^2 = 36
x^2 = 9
x = +3,-3


Hope you like the above example of Vertical Tangent.Please leave your comments, if you have any doubts.