Here, you will learn formula for binomial probability distribution in probability with example. Let’s begin – Suppose that we have an experiment such as tossing a coin or die repeatedly or choosing a marble from an urn repeatedly. Each toss or selection is called a trial. In any single trial there will be a probability …
Here, you will learn dependent and independent events in probability with examples. Let’s begin – Dependent and Independent Events Formula Two Events A and B are said to be independent if occurrence or non-occurrence of one does not affect the probability of the occurrence or non-occurrence of other. If the occurrence of one event affects …
Here, you will learn what is squeeze theorem or sandwich theorem of limit and limit of exponential function with examples. Let’s begin – Squeeze Theorem (Sandwich Theorem) If f(x) \(\leq\) g(x) \(\leq\) h(x); \(\forall\) x in the neighbourhood at x = a and \(\displaystyle{\lim_{x \to a}}\) f(x) = l = \(\displaystyle{\lim_{x \to 1}}\) h(x) then …
What is Squeeze Theorem – Limit of Exponential Functions Read More »
Here, you will learn how to find limit of trigonometric functions and limits using series expansion with example. Let’s begin – Limit of Trigonometric Functions \(\displaystyle{\lim_{x \to 0}}\) \(sinx\over x\) = 1 = \(\displaystyle{\lim_{x \to 0}}\) \(tanx\over x\) = \(\displaystyle{\lim_{x \to 0}}\) \(tan^{-1}x\over x\) = \(\displaystyle{\lim_{x \to 0}}\) \(sin^{-1}x\over x\) [where x is measured in …
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 …
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 …
Definition of Limit in Calculus – Theorem of Limit Read More »
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) …
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 …
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) …
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 …
