Let f (x) be a real valued function defied on an open interval (a, b) and let c ϵ (a, b). Then f (x) is said to be differentiable or derivable at x = c, if exist finitely.This limit is called the derivative or differential coefficient of the function f (x) at x = c, Read more about Differentiability at a Point[…]

Continuous Meaning: We say a function f (x) is continuous at a point x = a it means at a point (a, f (a)). The graph of the function has no holes or graphs. That is, its graph is unbroken at point (a, f (a)).The continuity at x = a2 if . does not exist. Read more about Continuity at a Point[…]

A function f is said to be discontinuous at a point a of its domain D if it is not continuous threat. The point a is then called a point of discontinuity of the function. The discontinuity may arise due to any of the following situations:a) or of both may not exist. b) as well Read more about Discontinuous functions[…]

A function f(x) is said to be continuous, if it is continuous at each point of its domain.Everywhere continuous function: A function f(x) is said to be everywhere continuous if it is continuous on the entire real line (-∞, ∞) i.e. On R. Some fundamental results on continuous functions: Here, we list some fundamentals result Read more about Continuous functions[…]

Angle between Line and a Plane: The angle between a line and a plane is the complement of the angle between the line and normal to the plane. Thus, if θ is the angle between a lines .And the plane ax + by + cz + d = 0. Then, the angle between the normal Read more about Intersection of Line and Plane[…]

A plane is a surface such that if any two points are taken on it, the line segment joining them lies completely on the surface. In other words, every point on the line segment joining any two points lies on the plane. Every first degree equation x, y and z represents a plane i.e., ax Read more about Equation of Plane and its different forms[…]

Let the equation of a plane be ax + by + cz + d = 0 When P and Q are on the same side of the plane ⇒ ⇒ ⇒ ax1 + by1 + cz1 + d and ax2 +by2 + cz2 + d are of the same sign. When P and Q are Read more about Distance of point from plane[…]

Centroid of Triangle: The coordinates of the centroid of the triangle with vertices A (x1, y1, z1) B (x2, y2, z2) and C (x3, y3, z3) Proof: Let D be the mid-point of AC then coordinates of D are Let G be the centroid of ΔABCThen, G divides AD in the ratio 2:1 So, coordinate Read more about Centroid of Triangle & Centroid of Tetrahedron[…]

Let v = a1 + λb1 and v = a2 + λb2 be the equations of two straight lines. If θ is the angle between them, then cos θ = , Also if θ is the angle between and , Then .Condition of perpendicularity: The lines are perpendicular, if b1 – b2 = 0 or Read more about Angle between Two Intersecting Lines[…]

Let l, m, n be direction cosines of a line and a, b, c be three numbers such that . Then we say that the direction ratios of the line are proportional to a, b, c. If ⅔, – ⅔, ⅓ are direction cosines of a line, then its direction ratios are proportional to 2, Read more about Direction ratios[…]