Proof of 0 = 1

ʃ tan(x) dx = ʃ sin(x) / cos(x) dx

ʃ tan(x) dx = ʃ sec(x) sin(x) dx [taking sec(x) as the 1st function]
ʃ tan(x) dx = - sec(x) cos(x) + ʃ sec(x) tan(x) cos(x) dx
ʃ tan(x) dx = - 1 + ʃ tan(x) dx
0 = - 1
0 + 1 = - 1 + 1
1 = 0

Nine Nine Nine Nine

Using only four 9s and standard arithmetic operations, it is possible to produce each of the numbers from 1 to 20.


For example,

1 = (9 + 9) / (9 + 9)

2 = (9 + √9) / (9 - √9)


Can you do the others?


(Kevin Hinks, Plymouth, MI)

Is 0.999 ... = 1 ?

Let C ...

We have,
1/3 = 0.333 ...
3 * (1/3) = 0.999 ...
1 = 0.999 ...

What do sin, cos, tan stand for?

Sin stands for Sine Function

Cos stands for Co-Sine Function
Tan stands for Tangent Function
Cot stands for Co-Tangent Function
Sec stands for Secant Function
Cosec or Csc stands for Co-Secant Function

(x+1) (x+3) (x+4) (x+6) = 72

Find the real root of (x+1) (x+3) (x+4) (x+6) = 72 if any.

The Near Misses

The Near Misses of Tendulkar
Runs	Against	Venue	Year
Tests
96	Sri Lanka	Bangalore	1994
92	West Indies	Bridgetown	1997
97	South Africa	Mumbai	2000
90	England	Bangalore	2001
92	England	Nottingham	2002
94	Pakistan	Mohali	2005
91	England	Nottingham	2007
98	Australia	Mohali	2010
91	England	Oval	2011
94	West Indies	Mumbai	2011
ODI
90	Australia	Mumbai	1996
91	England	Sharjah	1997
95	Pakistan	Dhaka	1998
93	Pakistan	Hobart	2000
93	South Africa	Nagpur	2000
93	Sri Lanka	Dhaka	2000
98	Pakistan	Centurion	2003
97	Sri Lanka	Johannesburg	2003
93	Sri Lanka	Nagpur	2005
95	Pakistan	Lahore	2006
99	South Africa	Belfast	2007
93	South Africa	Belfast	2007
99	England	Bristol	2007
94	England	Oval	2007
99	Pakistan	Mohali	2007
97	Pakistan	Gwalior	2007
91	Australia	Brisbane	2008
96*	Sri Lanka	Cuttack	2009