If `lim_(x rarr a)(x^9+a^9)/(x+a)=9`, find the real value of a.

lim_(x rarr 0) (|x|)/x is :

Find all possible values of a, if : lim_(x rarr a) (x^9-a^9)/(x-a)= lim_(x rarr 5) (4+x) .

If 27^x=9/3^x , find x.

Find all possible values of a, if : lim_(x rarr a) (x^3-a^3)/(x-a)= lim_(x rarr 1) (x^4-1)/(x-1) .

If 3^(4)xx9^(2)=9^(x) then the value of x is

3,x,9 are in A.P . Find the value of x

Let f(x) is a function continuous for all x in R except at x = 0 such that f'(x) lt 0, AA x in (-oo, 0) and f'(x) gt 0, AA x in (0, oo) . If lim_(x rarr 0^(+)) f(x) = 3, lim_(x rarr 0^(-)) f(x) = 4 and f(0) = 5 , then the image of the point (0, 1) about the line, y.lim_(x rarr 0) f(cos^(3) x - cos^(2) x) = x. lim_(x rarr 0) f(sin^(2) x - sin^(3) x) , is a. ((12)/(25),(-9)/(25)) b. ((12)/(25),(9)/(25)) c. ((16)/(25),(-8)/(25)) d. ((24)/(25),(-7)/(25))

If x+1 is a factor of ax^3+x^2-2x+4a-9 find the value of a

Evaluate : lim_(x rarr 0)(a^x-1)/(b^x-1) .

Find lim_(x rarr 0) f(x) , and lim_(x rarr 1) f(x) , where : f(x)= {(2x+3,",",xle0),(3(x+1),",", x>0.):}