`("lim")_(xvecpi/2)(a^(cotx)-a^(cosx))/(cotx-cosx)i se q u a lto` `ln a` (b) a (c) `lna/2` (d) does not exist

lim_(xrarrpi//2)(a^(cotx)-a^cosx)/(cotx-cosx)a gt 0 is equal to

("lim")_(xvec0)("cos"(tanx)-cosx)/(x^4)i se q u a lto 1/6 (b) -1/3 (c) 1/2 (d) 1

The value of lim_(xrar2pi)(cos x-(cosx)^(cosx))/(1-cos x+ln(cosx)) is equal to

For agt0, let l=lim_(xto(pi)/2)(a^(cotx)-a^(cosx))/(cotx-cosc) and m=lim_(xto-oo)(sqrt(x^(2)+ax))-(sqrt(x^(2)-ax)) then

>0,"l e t"& ell=lim_(x->pi/2)(a^(cotx)-a^(cosx))/(cotx-cosx)"and"m=lim_(x->-oo)(sqrt(x^2+a x)-sqrt(x^2-a x)) cot xcOS x16R cotx-cos y and m= LimxFor a > 0, let = Limax then-+ax-(A)is always greater than 'm' for all values of a >0(B) 'is always greater than 'm' only when a 21(C) 'e is always greater than 'm' for all values of 'a' satisfying a > e(D) e'+ m 0awepowivnaar noe s1021lauspo

21. If lim_(xrarroo) e^(x^2) - cosx / (sin^2x) is equal to (a) 3 (b) 3/2 (c) 5/4 (d) 2

(lim)_(nvecoo)1/x[int_y^a e^(sin^2t))dt-int_(x+y)^a e^(sin^2t))dt-]i se q u a lto (0,1] (b) [1,oo) (0,oo) (d) none of these

If A+B+C=pi , then the value of the determinant D=|sin^2AcotA1sin^2BcotB1sin^2CcotC1|i se q u a lto 1 (b) -1 (c) 0 (d) None of these

The value of lim_( x -> 0 ) ( 2^(-1/x^2)) is ( a ) 2 ( b ) 1/2 ( c ) 0 ( d ) does not exist

lim_(xto0) (log(1+x+x^(2))+log(1-x+x^(2)))/(secx-cosx)=