index of problems  with some classification  --------------index
integration

integral of sqrt(tanx)     -----> (integral of sqrt(tanx))

integral of coshx cosx       --------> (integral of cosh x cosx)

integral of (1+x) / x (x-2)^0.5       --------> (integral of (1+x) / x (x-2)^0.5)

integral of ln(sin x) from 0 to pi/2  ----------> (integral of ln(sin x) from 0 to pi/2)

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

 .∫ (x²) sin x  dx using integration by parts  ----------> (integration by parts)

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

∫ arc(tan4x) dx  ----------> (integration by parts)


∫ (sin3x)^4 dx  ----------> (integration by trignometric manipulation)

.∫ (x^4)(ln x)² dx ----------> (integration by parts)

∫ sec³x dx  ----------> (integration)

integrate 1/ (x^7 - x) -----------integration by adjusting
---------------------------------------------------------------
area

area bounded between the curves y=x^2+2 and y=3x   --------> (area between two curves)


---------------------------------------------------------------
differential equations


solve cot x (dy/dx) + y = csc x, with y(pi/3) = 0   --------> (linear differential equation)

solve x(dy/dx) + (1+x)y =2  (linear equation) --------> (linear equation)

solve y' -y =0 using power series method ------------>(power series method)


--------------------------------------------------------------------
--------------------------------------------------------------------------------------------------------------
(homepage)---------------(mixture)----------------(math)-------------(links)-----------(feedback)
--------------------------------------------------------------------------------------------------------------

mathematical induction

prove that (x-y) is a factor of (x^n -y^n ) ----------mathematical induction

proof of n^2 < 2^n for every integer n>=5     -----> (mathematical induction problem)

proof of 1^3 +2^3 + 3^3 +...+ n^3 = [ ( n (n+1) ) /2 ] ^2  -----> (mathematical induction problem)

1.2.3 + 2.3.4 + ... +n(n+1) (n+2) = n(n+1)(n+2)(n+3)/4 --------mathematical induction
---------------------------------------------------------------
partial fractions
put into partial fraction 1 / {(x^3) + 1 }     -----> (partial fractions problem)

put 1/[ (x)(x-2)(2x-1)] into partial fractions ----------partial fraction

---------------------------------------------------------------

trigonometry
prove that (cotA+cosecA-1)/(cotA-cosecA+1)=cosecA+cotA    -----> (problem on trigonometry )

Prove that (tanxsinx) / (tanx+sinx) = (tanx-sinx) / (tanx sinx)    -----> (problem on trigonometry )

find exact value of  tan[22½ °]   or tan (pi / 8 )      -----> (problem on trigonometry )

conditional identity : If A+B+C=π,
prove that: sinA+sinB+sinC = cot(A/2).cot(B/2) [sinA+sinB-sinC] -----> (problem on conditional identity (trigonometry) )


graphs of trigonometric functions-----> (graphs of trigonometric functions )

prove that
 { tan((π/4)+x) - tan((π/4)-x)} / { tan((π/4)+x) + tan((π/4)-x) } = sin2x ---------trigonometry problem

prove that  (cos²x - sin²x) / (cos²x + sinxcosx) = 1 - tanx -------------trigonometry problem

--------------------------------------------------------------
implicit differentiation
if sqrt(x) +sqrt(y) = 8, find dy/dx      ----------->( implicit differentiation )

differentiation from first principles
differentiate sqrt(x) from first principles     -----> (differentiation by first principles)
-------------------------------------------------------------
example on chain rule
differentiate ln(x + sqrt(x^2-1)) w.r.t.x     -----> ( derivative of ln(x + sqrt(x^2-1)))
-------------------------------------------------------------
example on uvw rule
find dy/dt if y = t exp(-t) [Acost +Bsint] -----------uvw rule
rateof change
lamppost-shadow problem ------>( lamppost-shadow problem)
-------------------------------------------------------------
example on maclaurin's series
maclaurin's series for sec(x)     -----> (maclaurin's series for sec(x))
-------------------------------------------------------------


invese laplace transforms
inverse laplace transform of  s / [(s+3)2 +1]    -----> (inverse laplace transorm problem)

inverse laplace transform of  1/ (s^2 + 1) ( s^2 - 2s + 7)    -----> (inverse laplace transorm problem)

-------------------------------------------------------------
limits
limit of (x^2-49)/(x^2+5x-14) as x-->( -7)    -----> (limit)

lim [e^(-ax)-e^(-bx)]/x   as x->0 -----> (limit)

limit (1-cosx) / x² as x-->0 ------- limt using trigonometry
-------------------------------------------------------------

sequence and series

Let S be the sum, P the product and R the sum of reciprocals of n terms in a G.P. Prove that P^2 R^n= S^n   -----> (g.p question)


Express  the recurring decimal 0.484848... as a fraction using the concept of geometric series  (infinite g.p question)
-------------------------------------------------------------

matrices

Solve by matrix inversion
x – y + 2z = 13
2x + 2y – z = -6
-x + 3y + z = -7  -----> (solution by matrix inversion)

-------------------------------------------------------------

remainder

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 x²-x-2 -----> (a problem on remainders)

find the quotient and remainder when x³ - 2x ² + 5x - 6  is divided by (x-3) using synthetic division-----> (a problem on long division)

-------------------------------------------------------------

problem on variance
show that var(aX+bY)=a²var(X)+b²var(Y) , if X and Y are independent ---------variance



(more problems)


(pictures of some fruits/ plants ) (index of math formulae)
-------------------------------------------------------------------------------------------------------
(homepage)---------------(mixture)----------------(math)-------------(links)-----------(feedback)
----------------------------------------------------------------------------------------