Find the total number of parallel tangents of `f_1(x)=x^2-x+1a n df_2(x)=x^3-x^2-2x+1.`

Find the range of f(x)=(x^2-x+1)/(x^2+x+1)

Which of the following pairs of expression are defined for the same set of values of x ? f_1(x)=2(log)_2xa n df_2(x)=(log)_(10)x^2 f_1(x)=(log)_xx^2a n df_2(x)=2 f_1(x)=(log)_(10)(x-2)+(log)_(10)(x-3)a n df_(2(x))=(log)_(10)(x-2)(x-3)dot

Find the range of f(x)=(x^2+1)/(x^2+2)

Let S be the set of all values of x for which the tangent to the curve y = f(x)= x^(3) - x^(2)- 2x at (x, y) is parallel to the line segment joining the points (1, f(1)) and (-1, f(-1)) , then S is equal to

Find the inverse of the function: f(x)={x^3-1, ,x<2 x^2+3,xgeq2

Find the sum to n terms of the sequence (x+1//x)^2,(x^2+1//x)^2,(x^3+1//x)^2, ,

Find the derivative of f(x)=1+x+x^(2)+x^(3)+…+x^(50)" at "x=1 .