Here, you will learn how to solve indeterminate forms of limits and general methods to be used to evaluate limits with examples. Let’s begin – Indeterminate Forms of Limits \(0\over 0\), \(\infty \over \infty\), \(\infty – \infty\),\(0\times \infty\), \(1^{\infty}\), \(0^0\), \({\infty}^0\) Note : (i) Here 0, 1 are not exact, infact both are approaching to […]
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Here, you will learn definition of limit in calculus, left hand limit, right hand limit and fundamental theorem of limit. Let’s begin – Definition of Limit in Calculus Let f(x) be defined on an open interval about ‘a’ except possibly at ‘a’ itself. If f(x) gets arbitrarily close to L(a finite number) for all x
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Here, you will learn different types of ellipse and their basic definitions with their graphs. Let’s begin – Different Types of Ellipse (a) First type of Ellipse is \(x^2\over a^2\) + \(y^2\over b^2\) = 1, where a > b (a) AA’ = Major axis = 2a (b) BB’ = Minor axis = 2b (c)
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Here, you will learn trigonometric equations solving strategies i.e by factorisation and reducing it to a quadratic equation etc. Let’s begin – Different Strategies for Trigonometric Equations Solving (a) Solving trigonometric equations by factorisation Example : If \(1\over 6\)sin x, cos x, tan x are in G.P. then the general solution for x is Solution
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Here, you will learn what is vector triple product formula and linear independence and dependence of vectors. Let’s begin – Vector Triple Product Formula Let \(\vec{a}\), \(\vec{b}\) and \(\vec{c}\) be any three vectors, then the expression \(\vec{a}\times (\vec{b}\times\vec{c})\) is a vector & is called a vector triple product. Linear Independence And Dependence of Vectors (a)
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Here, you will learn formula for conditional probability and properties of conditional probability with examples. Let’s begin – Formula for Conditional Probability Let A and B be two events associated with a random experiment. Then, the probability of occurrence of event A under the condition that B has already occured and P(B) \(\ne\) 0, is
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Here, you will learn probability basic concepts and definitions of probability. Let’s begin – Probability gives us a measure of likelihood that something will happen. However probability can never predict the number of times that an occurrence actually happens. Probability Basic Concepts and Definitions (a) Experiment : An action or operation resulting in two or
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Here, you will learn equation of family of lines and the combined equation of the bisectors of the angle between the lines. Family of Lines Equation If equation of two lines be P = \(a_1x+b_1y+c_1\) = 0 and Q = \(a_2x+b_2y+c_2\) = 0, then the equation of the lines passing through the point of intersection
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Here, you will learn equation of straight lines in all forms i.e. slope form, intercept form, normal form and parametric form etc. Let’s begin – A relation between x and y which is satisfied by co-ordinates of every point lying on a line is called equation of the straight lines. Here, remember that every one
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Here, you will learn formula for angle between two lines, equation of straight line making an angle with a given line and reflection and image of a point in a line and also length of perpendicular from a point on a line. Let’s begin – Angle between Two Lines (a) If \(\theta\) be the angle
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