lf `a ,b , in {1,2,3,4,5,6,},` find the number of ways `a` and `b` can be selected if `lim_(x->0)((a^x+b^x)/2)^(2/x)=6.`

If a,b,c in{1,2,3,4,5,6,} find the number of ways a,b,c can be selected if f(x)=x^(3)+ax^(2)+bx+c is an increasing function.

If a,b are chosen from {1,2,3,4,5,6,7} randomly with replacement. The probability that lim_(x to0) ((a^x+b^x)/2)^(2//x)=7 is

lim_(x rarr0)(3x^(2)+5x-1)/(x^(2)+2x+6)

Evaluate lim_(x rarr0)((a^(x)+b^(x)+c^(x))/(3))^(2/x);(a,b,c>0)

If a and b are chosen randomly from the set consisting of number 1, 2, 3, 4, 5, 6 with replacement. Then the probability that lim_(x to 0)[(a^(x)+b^(x))//2]^(2//x)=6 is

Evaluate: lim_(xrarr2) (x^(3)-2x^(2))/(x^(2)-5x+6)

Evaluate : lim_(x rarr2)(x^(2)-5x+6)/(x^(2)-4)

find a&b if lim_(x rarr oo)((x^(2)+1)/(x+1)-ax-b)=0

Find the values of a\ &\ b : (lim)_(x->oo)[(x^2+1)/(x+1)-a x-b]=0