curve sketching

Let us learn about curve sketching

Sketch the curve
y = - sin 2x ….(1)
Symmetry

(a) By replacing y by -y, the equation (1) is altered; so the curve is not symmetrical about x-axis.

(b) By replacing x by –x & the equation of the curve is altered; so the curve is not symmetrical about y-axis.

(c) Replace x & y by -x and -y respectively in the equation y = - sin 2x, the equation of the curve remain unaltered. So the curve is symmetrical in opposite quadrants.

The term “curve sketching” referred as using calculus to help draw the graph of a function by hand – the graph was the goal. Hence graphs can now be produced with great precision using computers & calculators.

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matrix properties

Let us learn about matrix properties

The invertible matrix properties represent the properties which explain the matrices that are invertible that is which matrices are compatible to find out the inverse of the matrix in detail. Some properties involved in the invertible matrix are mentioned below

• The invertible matrix must be square - matrix.
• The invertible matrix must be the non - singular matrix.
• The determinant value should not be “0” zero.

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hypotenuse calculator

Let us solve problem using hypotenuse calculator

The Hypotenuse Calculator makes it simple to find the length of any hypotenuse

The hypotenuse calculator can be found using the Pythagorean Theorem which states that a^2 + b^2 = c^2. Square the 2 sides add them together then find the square root to calculate the hypotenuse. A hypotenuse is referred as the side of a right triangle opposite the right angle

Use hypotenuse calculator to find the hypotenuse of the triangle when the 2 sides are a=8cm & b=6cm

Right angle triangle

a=8cm & b=6c, if we substitute the side values a & b in the calculator, then we get the hypotenuse value.

Using Pythagorean Theorem, we have to use hypotenuse calculator to find the hypotenuse.

: a² + b² = c²

8² + 6² = c²

64+36= c²

100= c²

C=10cm

Therefore the hypotenuse of the triangle is c=10cm.

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tan x

Let us learn about tan x

Trigonometry is referred as a branch of mathematics which studies triangles. Trigonometry also deals with the relationships between the sides & angles of triangles & deals with trigonometric functions, that describe those relationships, angles in general, & the motion of waves.
The branch of mathematics which deals with the association between the sides & the angles of triangles & the calculations based on them, predominantly the trigonometric functions.
Trigonometry is a branch of mathematics which learns the trigonometric functions of angles, cosine, tangent, sine, cotangent, secant, cosecant & the relationship between them. 1 of its applications is surveying & navigation.
Trigonometric functions are also known as circular functions because of their simple relation to various lengths defined by a radius of a circle making an angle with a reference direction,
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math homework help for free

Let us learn about math homework help for free

Math homework help for free gives us the opportunity to practice what we are learning in class. When we do Math homework we learn which skills we don't fully understand. We can also discover new ways & methods of approaching a problem. Math Homework does not just aid our learning it also helps us study for those inevitable tests & quizzes which do determine our grades.

Math Homework has been a part of students' life from the beginning of formal school. However, the practice has sometimes been accepted & other times rejected, both by parents & educators. This has happened because Math homework can have both negative & positive effects on learner's learning & attitudes towards school. Some tutors view that math homework should not be given to students. Giving Math homework means creating learning environment like school mania at home. Others educators are of the view that five hours in the school is in sufficient & it must be supplemented by some work at home. It is not the math homework that is objectionable, but its nature & amount which invites criticism. But the importance & need of math homework cannot be minimized, if it is of a right nature.

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slant asymptote

Let us learn about slant asymptote

Try to find the slant asymptote of the following function:

Y = x² + 3x + 2 divided by x – 2

To find the slant asymptote, we need to do the long division:

The slant asymptote is the polynomial part of the solution, not the remainder.

Slant asymptote: y = x + 5

Just like horizontal & vertical asymptotes, slant asymptotes are lines the graph approaches. Slant asymptote are also called oblique asymptotes.

A graph always has a slant asymptote if the degree of the numerator is bigger than the degree of the denominator

If you want to find slant asymptotes, divide the numerator by the denominator & keep only the quotient Don't forget that these are still lines, so slant asymptote are written as y =

To divide slant asymptote, you either have to use long division or synthetic division

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multiples of 9

Let us learn about multiples of 9

The multiples of a whole number are found by including the product of any counting number & that whole number. There are an infinite number of multiples of 9. A multiple is what we get when we multiply something. The multiples of 9 are:

9, 18, 27, 36, 45, 54, 45, 63, 72, 81, 90, & so on, going up by 9 each time forever.

9,18,27,36,45,54,63,72,81,90,99,104 the rest of the multiples would be 18, 27, 36... etc It mainly depends which multiple. The multiples of nine up to 90 are:

9, 18, 27, 36, 45, 54, 63, 72, 81, 90

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