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Longest Rivers of the World
RANK River Region Length (KM/MILES) 1 The Nile East and North Africa (7,088 KM / 4,404 MILES) 2 Amazon South America (Peru, Colombia, Brazil ) (6,992…
5 Minute Guide to ERP3
Information technology has transformed the way we live and the way we do business. ERP, or Enterprise Resource Planning, is one of the most widely implemented…
Even & Odd Functions
A function is said to be an even function if the sign of the image does not change when the sign of the preimage changes. Conversely,…
Characteristics of a chemical reaction.
A chemical reaction generally has one or more of the below-mentioned characteristics. 1> Change in stateCertain chemical reactions are featured with a change in the state…
What is a Chemical Reaction?
A process in which one or more substances get transformed to produce new substance or substances is called a Chemical Reaction. A chemical reaction involves changes…
Probability Cause and Effect Problem
Question What does it mean for one event ? to cause another event ? – for example, smoking (?) to cause cancer (?)? There is a…
Probability Problem: Suppose you roll a fair die two times. Let ? be the event "THE SUM OF THE THROWS EQUALS 5" and ? be the event "AT LEAST ONE OF THE THROWS IS A 4". Solve for the probability that the sum of the throws equals 5, given that at least one of the throws is a 4. That is, solve ?(?|?).
Solution We have A = (1,4), (2,3), (3,2), (4,1) B = (1,4), (2,4), (3,4), (4,4), (5,4), (6,4), (4,1), (4,2), (4,3), (4,5), (4,6) \( P(A|B) = \dfrac…
THEOREM# \( \lim_{\theta\to0} \dfrac{sinθ}{θ} \) = 1
We have \( \lim_{\theta\to0} { \sin\theta \over \theta } \) = 1 Consider the below diagram. We have r = radius of the circle.A = centre…
Theorem# \( \lim_{x \to a} { x^n – a^n \over x – a } = na^{n-1} \)
To prove : lim\( _{x \to a} { x^n – a^n \over x – a } = na^{n-1} \) where n is a rational number Proof:…
Theorem# Limit of tanθ as θ → 0
Proof : We have, lim\(_{θ\to 0} { \dfrac {\mathrm tan \mathrm θ}{ \mathrm θ} } \) = lim\(_{θ\to 0} { \dfrac {\mathrm \sin \mathrm θ} {\mathrm…
Theorem# Limit of cosθ as θ → 0
As θ → 0, we have cosθ → 1 Proof : When θ = 0, We have, lim\(_{θ\to 0} \cos \)θ = cos0 = 1 {…
Derivative of \(\mathsf { x^{n} }\) using the First Principle
Let y = \(\mathsf {x^{n} }\) ∴ y + δy = \(\mathsf { {(x + δx)^{n}} }\) ∴ δy = y + δy – y =…
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