Calculus Answers

Find lim x->infinite 2/x.

Check whether the function f : R→R given by f (x) =| x | −[x], is a bijective. Give reasons for
your answers.

Show that f, given by
f(x)={ x sin 1/x,x not equal to zero, 0,x=0 is continuous at each point of R.

Find the angle between the y-axis and the tangent to the hyperbola xy =1 at (1, 1).

Evaluate lim x ->1(1/(1-x) -1/(1-x[sup]2[/sup]))

Find the point of which the function f, defined below, is continuous in ]−infinite,infinite[ . f(x) = { x^2 /a -a ;x less than and equal to a , a is not equal to zero , a-a^2/x ; x>a

f : R→R, given by f (x) = 2 | x |−1, is differentiable on R.

Prove that the function f, defined by f(x)=x sinx + cosx, is decreasing in [0,pi/2].