Let `a=2010^(log_(2011)(2012)), b=2010^(log_(2012)(2011)` and `c=(2010)^2` then which of the following is the alternative?

Let f(x)=lim_(n rarr oo)(sin x^(2012)+(1+x^(2011))^(n)tan x^(2011))/(cos x^(2012)+(1+x^(2011))^(n)),n in N then which of the following is(are) true?

Let P=log_(0.3)((a-a^(-1))/(2)) a where a=tan((3 pi)/(8)) and Q=log_(cos(2 pi)/(3))b=sec2010 pi ,then which of the following is true?

Simplify ((2011^(2)-2017)(2011^(2)+4022-3)(2012))/(2013.2014.2008.2010)

Let f be a function defined on R (the set of all real numbers) such that f'(x)=2010(x-2009)(x-2010)^(2)(x-2011)^(3)(x-2012)^(4) for all x in R. If g is a function defined on R with values in the interval (0,oo) such that f(x)=ln(g(x)), for all x in R , then the number of point is R at which g has a local maximum is

Let f be a function defined on R (the set of all real numbers) such that f^(prime)(x)=2010(x-2009)(x-2010)^2(x-2011)^3(x-2012)^4, for all x in Rdot If g is a function defined on R with values in the interval (0,oo) such that f(x)=ln(g(x)), for all x in R , then the number of point is R at which g has a local maximum is ___