TOPMATH.IN
some problems in mathematics and their solution, mathematical formulae and many other things that I like

started on 25-4-2017


Important Formulae

* Indices, surds and some identities:

* Quadratic equations

* Complex Number

* Progression

* Trigonometry formula

*Analytical Geometry

*list of differentiation formula

*integral calculus integration formula

*Vector

*Hyperbolic function

*Laplace Transform Inverse laplace transform

*correlation coefficient equation of regression line

*Indeterminate forms, LHospital's rule, Permutation and Combination

*square root without using calculator by using long division method

* Sign of trigonometry ratios in different quadrant  ratio
for [(pi/2) - x] , [(pi/2) + x], [pi - x],[pi + x],[(3pi/2) - x] , [(3pi/2) + x],[2pi - x],[- x]


* Graph Theory definitions
mixture:
*interesting things about north korea  and south korea


*lice infestation or louse infestation


*road salt

*disaster at lake nyos in cameroon

*sahara desert

*pointless

*some things to know about haiti ,
the haitian revolution

*newborn baby

MUSIC

*elvis presley

question
* list of problems and questions on mathematics

Integration

* Integrate e^{x^(1/3)}dx

* evaluate integral of [e^(-x) +1] ^2

*evaluate ∫ (sin 3x)^4 dx with limits 0 to pi

*the integral of (1+x) /[ x *sqrt(x-2)]

* evaluate the integral of sqrt(tan  x)

* evaluate integral of { sqrt{1+(x^2)} } / {x^2}
using integration by parts


*∫ secx dx using integration by parts

*integral of (e^(ax) )  cosbx using integration by parts

*∫ arc(tan4x) using integration by parts

*evaluate the integral of coshx cosx by integration by part method

*evaluate .∫ (x) sin x  dx using integration by parts

*evaluate .∫ x cos(mx) dx using integration by parts

*integral of log(sin x) from 0  to pi/2 (where the log is of base e)




Area using integral

* evaluate the area of an ellipse (x /a) + (y/b) =1 using integration

* find the area between y = x and x =y

* find the area bounded b y =x and y = 3x

Differential equation

*solve x(dy/dx) + (1+x)y =2





Differentiation
differentiation from first principles
*differentiate sqrt(x) from first principle

*if y = x sinx , find dy/dx from first principles

*find the derivative of f(x) =1/x at x=3 using the
lim {f(x)-f(a)} / {x-a} as x---->a



*derivative of ln(x + sqrt(x^2-1))

Implicit differentiation

*find dy/dx if sqrt(x) +sqrt(y) = 8

*if  xy + y^2 =1 , find dy/dx

*if √(xy) = x - 2y, find dy/dx using implicit differentiation

Differentiation using trigonometric substitution 
*differentiate. arctan √ [(1-x)/(1+x)] w.r.t..x using trigonometric substitution



Application of differential calculus
* power series expansion for y = arctan(x) in powers of x

*find the maclaurin series for sec x



Boolean Algebra
*show that (p v q) → r ≡ (p → r) ^ (q→ r)

Mathematical Induction


*Prove that [1/(1x2) ]+[1/(2x3)]+...+ [1/( n(n+1) )] = n/n+1
using mathematical induction)


*prove by mathematical induction
 that 1^3 +2^3 + 3^3 +...+ n^3 = [ ( n (n+1) ) /2 ] ^2


Partial fraction
*put into partial fraction 1 / { (x^3) + 1 }

Algebra
*When a polynomial p(x) is divided by (x+1), the remainder is 4.
And when it is divided by (x-2), it's remainder is 3.
What is the remainder  when p(x) is divided by x-x-2


*Express  the recurring decimal 0.484848... as a fraction
 using the concept of geometric series

*If the sum of two consecutive odd integers is 20,
find the numbers


*Factorise 2(x^3) - 3 (x^2)  - 3x +2



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