X Xx

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My question is Show that lim x rightarrow c frac x c c x x x c c exists and find its value Because the limit is 0 0 I ve tried using L Hopital s rule but every time I differentiate it I still

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I am a 12th grade student and I am afraid that in realistic terms this question might not even make sense because of the infinities that have to be dealt with However in my attempt to calculate

https://math.stackexchange.com › questions › xx-y-how-to-solve-for-x
You want to solve xx c x x c for some number c c The answer x x cannot be expressed in terms of the common functions polynomials trigonometric functions exponential etc but you can

https://math.stackexchange.com › questions › differentiation-of...
How is differentiation of xx T with respect to x as 2x T where x is a vector x T means transpose of x vector

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The way I am thinking that while x T is the transpose of x then we cross product with itself using x T which results in a symmetric matrix R So R is a square matrix

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How would I go about solving equations of this form x x n for values of n that do not have obvious solutions through factoring such as 27 3 3 or 256 4 4

https://math.stackexchange.com › questions › limit-of-xx-as-x...
You have basically two options Allow complex arguments then the limit doesn t exist or restrict to positive or non negative arguments Then lim limits x searrow 0 e x log x settles the matter

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Note that you can show directly that X TX T X TX without diving down into individual elements but I wanted to highlight the fact that this matrix contains all of the possible dot

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2 If x has length 1 then xx T is the orthogonal projection on the subspace of mathbb R n endowed with the canonical scalar product generated by x