If `y=1/(t^2+t-2),w h e r et=1/(x-1),` then find the number of points where `f(x)` is discontinuous.

Consider the equation 2/x+5/y=1/3w h e r ex ,y in Ndot Find the number of solutions of the equation.

If f(x+2a)=f(x-2a),t h e np rov et h a tf(x)i sp e r iod i cdot

Find the points of minima for f(x)=int_0^x t(t-1)(t-2)dt

If f(x)=x^n ,f(1)+(f^1(1))/1+(f^2(1))/(2!)+(f^n(1))/(n !),w h e r ef^r(x) denotes the rth order derivative of f(x) with respect to x , is

For the hyperbola (x^2)/(a^2)-(y^2)/(b^2)=1 , let n be the number of points on the plane through which perpendicular tangents are drawn. If n=1,t h e ne=sqrt(2) If n >1,t h e n0 sqrt(2) None of these

Let z=t^2-1+sqrt(t^4-t^2),w h e r et in R is a parameter. Find the locus of z depending upon t , and draw the lous of z in the Argand plane.

f(x)=int_1^x(tan^(-1)(t))/t dt , x in R^+, then find the value of f(e^2)-f(1/(e^2))

Find the points of discontinuity of the function: f(x)=1/(2sinx-1)

Find the continuous function f where (x^4-4x^2)lt=f(x)lt=(2x^2-x^3) such that the area bounded by y=f(x),y=x^4-4x^2dot then y-axis, and the line x=t , where (0lt=tlt=2) is k times the area bounded by y=f(x),y=2x^2-x^3,y-a xi s , and line x=t(w h e r e0lt=tlt=2)dot

If y=f(x)=((x+3))/((x-1)),t h e n x=f(y) (b) f(1)=3 y increases with xforx<1 f is a rational function of x