Hyperbolic functions are analogs of the ordinary trigonometric, or circular, functions. They are defined in terms of the exponential function and are important in many areas of mathematics, including algebra, geometry, calculus, and complex analysis. Hyperbolic functions are closely related to the exponential function, as evident from their definitions. The basic hyperbolic functions are: Definition […]
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First lets us see what is Modulus function and then we will see how to do Integration of modulus function What is modulus function Modulus Function is defined as the real valued function $f : R \rightarrow R$ , y = |x| for each $x \in R$ For each non-negative value of x, f(x) is
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Integration of sec x can be found using various integration technique like integration by substitution, Integration by partial fraction along with trigonometric identities. The various formula for integration of sec x are I \[\int \sec(x) \, dx = \ln | \sec(x) + \tan(x) | + C\] II \[\int \sec(x) \, dx = -\ln | \sec(x)
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Integration of tan x can be found using various integration technique like integration by substitution along with trigonometric identities. The formula for integration of tan x is \[\int \tan(x) \, dx = \ln |sec(x)| + C\] Proof of the Integration of tan x Integration of tan x can be solved using integration by substitution as
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Number 45 is a composite number and we will find how to find the factors of 45. We will also see techniques to find out the Prime factorization of 45 easily Factors of 45 A factor of a number is an exact divisor of that number. So factors of 45 are the numbers which are
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Number 24 is a composite number and we will find how to find the factors of 24. We will also see techniques to find out the Prime factorization of 24 easily Factors of 24 A factor of a number is an exact divisor of that number. So factors of 24 are the numbers which are
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Differentiating trigonometric functions is a fundamental concept in calculus. Here’s a quick guide to the derivatives of the basic trigonometric functions. Assume that x is a variable and all functions are differentiable. Differentiation of Trigonometric Functions Important formula to find the derivative$\frac {d}{dx} f(x) =\displaystyle \lim_{h \to 0} \frac {f (x+h) – f(x)}{h}$$\displaystyle \lim_{x \to
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The integration of the greatest integer function, often denoted as [x], where x is a real number, can be a bit tricky because the function is not continuous. The greatest integer function returns the largest integer less than or equal to x. For example,[1.2] = 1[-1.1] = -2[4.5]=4[.5]=0[-.2]=-1[2]=2 Integration of greatest integer function To integrate
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