`lim_(x->0)(1-sqrt(cos2x)*root(3)(cos3x).....root(n)(cosnx))/x^2` has value `10`, then value of `n` equal to

lim_(x rarr0)(1-sqrt(cos2x)*root(3)(cos3x)...root(n)(cos nx))/(x^(2))

If lim_(x rarr0)(1-cos x*cos2x*cos3x...cos nx)/(x^(2)) has the value equal to 263, find the value of n ( where n in N)

lim_(x rarr0)(sqrt(1+x)-sqrt(1-x))/(root(3)(1+x)-root(3)(1-x))

lim_(x rarr0)(sqrt(1+x)-sqrt(1-x))/(root(3)(1+x)-root(3)(1-x))

lim_(x rarr0)(sqrt(1+x)-sqrt(1-x))/(root(3)(1+x)-root(3)(1-x))

If cos^(-1)(cos x)=(n-x)/n,xge0 , has seven roots, then find values of n.

If lim_(x rarr0)(1-cos(1-cos(1-cos x)))/(x^(a)) exists and has a non-zero value,find the value of a.

If the value of lim_(xto0) (2 - cosx sqrt(cos2x))^(((x+2)/(x^(2)))) is equal to e^(a) then a is equal to _______ .

lim_(x ->oo)x^(2)(sqrt((x+2)/(x))-root(3)((x+3)/(x))) equals

lim_(x rarr0)(sqrt(1-cos2x))/(2x) is equal to =