Prove that, f(x)`=(1-2x-x^(2))/(1+x-2x^(2))` continually diminishes as x continually increases.

If f(x)=2x-tan^(-1) x-log (x+sqrt(x^(2)+1)) , then show that f(x) steadily increases as x increases from zero to positive infinity and hence deduce that, 2x gt tan^(-1) x+log (x+sqrt(x^(2)+1))

For what value of f (4) the function f(x)=(x^(2)-16)/(x-4) is continuous at x = 4 ?

Prove that the function f (x) = 5 is continuous at x = 2 .

Draw the graph of the function f(x)=(x^2-1)/(x-1) and from the graph examine whether f(x) is continuous at x = 1 and x = 2.

The value of f(0) so that the function f(x)=frac(2x-sin^-1x)(2x+tan^-1x is continuous at each point in its domain is equal to

If f(x)=x-2, x le 0 and 4-x^2,x > 0, then discuss the continuity of y=f(f(x)).

If the function f: R- {0}-> R given by f(x)=1/x-2/(e^(2x)-1) is continuous at x=0, then find the value of f(0)

Show that the function f(x)=5x-|2x| is continuous at x = 0

The function f(x)=(x^(2)-4)/(x^(3)-8) is undefined at x =1 , what should be the value of f (1) such that f (x) may be continuous at x =1 ?

Let f(x)={{:((1)/(x^(2))sin(x^(2))," when "xne0),(0," when " x=0):} Discuss the continuity of f (x) at x = 0 .