Category: Calculus

Radius of curvature of the curve y = f(x) is given by Example 01: Find the radius of curvature of the curve y = x3 at (2, 8) Solution: Equation of curve is y = x3 ………. (1) Differentiating both sides w.r.t. x  (dy/dx) = 3×2 ………………. (2) (dy/dx) at P(2, 8) = 3(2)2 = […]

In this article, we shall study to form a differential equation by eliminating a single arbitrary constant from the given relation. Example – 01: xy = c Solution: Given xy = c ……….. (1) Differentiating both sides w.r.t. x x + y(1) = 0 ∴ x + y = 0 This is the required differential Equation […]

In this article, we shall find the maximum and minimum value of the given function. Example – 01: If x + y = 3 show that the maximum value of x2 y is 4 Solution: Given x + y = 3 hence y = 3 – x ∴  x2 y = x2(3 – x) = 3×2 – x3 […]

In this article, we shall study to find the displacement, velocity, and acceleration of a particle, by the calculus method. Example – 01: A particle is moving in such a way that is displacement ’s’ at any time ‘t’ is given by s = 2t2 + 5t +20. Find the velocity and acceleration of the […]

In this article, we shall study the concept of maximum and minimum values of a function using the concept of differentiation. Example – 01: Find the maximum and minimum values of x3 – 12x – 5 Solution: Let ƒ(x) = x3 – 12x – 5 ………….. (1) Differentiating equation (1) w.r.t. x ƒ’(x) = 3×2 […]

In this article, we shall study more examples to find the equation of normal and tangent to a curve at a given point. Example – 12: Find the equation of the tangent and normal to the curve x = sin θ and y = cos 2θ at θ = π/6 Solution: The equation of the […]

In this article, we shall study the use of the concept of differentiation to find slope, equation of tangent, and normal. Example – 01: Find the equation of the tangent and normal to the curve y = 3×2 – x + 1 at point P(1, 3) Solution: Equation of curve is y = 3×2 – […]

In the last article, we have studied the concept of the function and the terminology associated with it. In this article, we shall study different types of functions. Real Function: A function whose domain and co-domain are the set or subset of real numbers R, then the function is called a real function.Thus if ƒ: […]

Function or Mapping: Let A and B two non-empty set and If each and every element x of set A is related by the relation ‘ƒ’ to one and only one element y of the set B such that y = ƒ(x) then such a relation ƒ from set A to set B is called […]