Show by example that although f and g may fail to have a limit at a cluster point c, their sum f+g can have a limit at c. Give similar examples for the product fg and for the quotient f/g. Please provide detailed answers. Solution let f(x)= sec^2x let g(x) = -tan^2x then f+g will give constant \'1\' Notice that these do not limit at pi/2 but f+g does have a limit everywhere. Similarly for product, f=tan(x) does not exist around pi/2, but when multiplied with g =cos(x) , they give value sin(x), which has limit everywhere Similarly, g(x)=(1/x) has no limit at x=0, f(x) = x, but f/g = x^2 has limit everywhere..