Let `a_1`, `a_2`... . . `a_n` be fixed real numbers and define a function `f(x)= (x -a_1 )(x-a_2 )...(x -a_n).` What is ` lim_(x rarr a_1)f(x)`? For some `a ne a_1,a_2,....a_n`, compute `lim_(x rarr a)f(x)` .

if f(x) = (x - a_1) (x - a_2) .....(x - a_n) then find the value of lim_(x to a_1) f(x)

If the function f(x) satisfies lim_(x rarr 1)(f(x)-2)/(x^2-1)=pi , evaluate lim_(x rarr 1) f(x) .

If the function f (x) satisfies lim_(x rarr 1)(f(x)-2)/(x^2-1)=pi , evaluate lim_(xrarr1)f(x) .

Consider the function : f (x) ={(x+2, x ne 1),(0,x=1):} . To find lim_(x to 1) f(x) .

Let f(x)= (sqrt(x+3))/(x+1) , then the value of lim_(x rarr -3^-) f(x) is :

If f(x)={(mx^2+n, x 1):} . For what integers m and n does both lim_(x rarr 0)f(x) and lim_(x rarr 1)f(x) exist?

If a_1,a_2,a_3,....a_n are positive real numbers whose product is a fixed number c, then the minimum value of a_1+a_2+....+a_(n-1)+3a_n is

If a_1,a_2,a_3,.....,a_(n+1) be (n+1) different prime numbers, then the number of different factors (other than1) of a_1^m.a_2.a_3...a_(n+1) , is

Find lim_(x rarr 1)f(x) where f(x)= {(x^2-1,xle1),(-x^2-1,x>1):}

Let a_1, a_2 ,........ be positive real numbers in geometric progression. For each n, let A_n, G_n, H_n be respectively the arithmetic mean, geometric mean and harmonic mean of a_1,a_2..........a_n . Find an expression ,for the geometric mean of G_1,G_2,........G_n in terms of A_1, A_2,........ ,A_n, H_1, H_2,........,H_n .