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3 days ago · Using the substitution rule gives. \lim_ {x \rightarrow 3}\dfrac {x^2-9} {x-3}=\frac {3^2-9} {3-3}=\frac {0} {0}, x→3lim x−3x2 −9 = 3−332 −9 = 00, which is an indeterminate number. Limits that end in an indeterminate number like the example above are said to be in indeterminate form.
Using the direct substitution method means that we compute the limit of the function by finding the function value. Using limit notations, the direct substitution tells us that, for an eligible function 𝑓 ( 𝑥), l i m → 𝑓 ( 𝑥) = 𝑓 ( 𝑎). In this example, 𝑓 ( 𝑥) = − 9 𝑥 − 6 𝑥 − 9 and 𝑎 = − 5.
Factorize this equation: f (x,y,z) = x^2 (y-z) + y^2 (z-x) + z^2 (x-y).\qquad (1) f (x,y,z) = x2(y −z)+y2(z −x)+z2(x −y). (1) We know that f (x, y, z) f (x,y,z) is a cyclic polynomial because f (x, y, z) = f (y, z, x) = f (z,x,y) f (x,y,z) = f (y,z,x) = f (z,x,y). We can note that f (y, y, z ) = 0 f (y,y,z) = 0.
5 days ago · The chain rule states that the derivative of their composite at the point x = a is: In Leibniz's notation, this is: or for short, The derivative function is therefore: Another way of computing this derivative is to view the composite function f ∘ g ∘ h as the composite of f ∘ g and h.
2 days ago · The usual treatment (e.g., Albert Einstein's original work) is based on the invariance of the speed of light. However, this is not necessarily the starting point: indeed (as is described, for example, in the second volume of the Course of Theoretical Physics by Landau and Lifshitz), what is really at stake is the locality of interactions: one supposes that the influence that one particle, say ...
5 days ago · How did the election of 1876 solve an immediate political crisis, and did that solution indicate that the Reconstruction amendments had failed to achieve their goals? This lesson examines how the election of 1876 marked the end of Reconstruction and the beginning of the backsliding of political, social, and economic advancements made by freed ...
3 days ago · A differential equation. y + p(x)y = g(x)yα, where α is a real number not equal to 0 or 1, is called a Bernoulli differential equation. It is named after Jacob (also known as James or Jacques) Bernoulli (1654--1705) who discussed it in 1695. Jacob Bernoulli was born in Basel, Switzerland. Following his father's wish, he studied theology and ...
