GATE Questions & Answers of Limit, Continuity and differentiability

What is the Weightage of Limit, Continuity and differentiability in GATE Exam?

Total 5 Questions have been asked from Limit, Continuity and differentiability topic of Calculus subject in previous GATE papers. Average marks 1.40.

limxx+sinxx equals to

With reference to the conventional Cartesian (x, y) coordinate system, the vertices of a triangle have the following coordinates: (x1, y1) = (1, 0); (x2, y2) = (2, 2); and (x3, y3) = (4, 3). The area of the triangle is equal to

The expression lima0xa-1a is equal to

What should be the value of λ such that the function defined below is continuous at x=π2

fx=λcosxπ2-xifxπ21ifx=π2

The limx0sinx32x is