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Question #2065

Check whether the function f : R→R given by f (x) =| x | −[x], is a bijective. Give reasons for
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**1.**Show that f, given by f(x)={ x sin 1/x,x not equal to zero, 0,x=0 is continuous at each…**2.**Find the angle between the y-axis and the tangent to the hyperbola xy =1 at (1, 1).**3.**Evaluate lim x ->1(1/(1-x) -1/(1-x[sup]2[/sup]))**4.**Find the point of which the function f, defined below, is continuous in ]−inf…**5.**The slope of the tangent of the curve y = x/x[sup]2[/sup] +2 , at the origin is 0.**6.**f : R→R, given by f (x) = 2 | x |−1, is differentiable on R.**7.**Prove that the function f, defined by f(x)=x sinx + cosx, is decreasing in [0,pi/2].

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