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Show that the function $f:mathbb Rrightarrow mathbb R$ defined by $f(x)=x^2sin frac {1}{x}$ if $xneq 0$ and $f(0)=0$ is surjective. What I thought that if I...
Asked on 11/26/2020 by Mathfun
2 answer$x+y = 5$ and $x+7 = y^2$.$$$$It is possible to calculate the area between two curves as follows: $int_a^b f(x) dx$ + ...
Asked on 11/26/2020 by Diego Lima
1 answercan i solve this limit using polar coordinate?$$lim_{(x,y)toinfty} frac{x^2+y^2}{x^2+(y-1)^2}=$$$$frac{r^2}{r^2-2rsintheta +1}=frac{1}{1-frac{2sintheta}{r}+frac{1}{r^2}}=1$$...
Asked on 11/26/2020 by simon
1 answerI'm trying to find triplets of integer $(x, y)$ pairs - $(x_1, y_1), (x_2, y_2), (x_3, y_3)$ - that satisfy the following equations: $${x_1}^2 + {y_1}^2...
Asked on 11/26/2020 by GodOrGovern
0 answerFrom the axioms I remember about vector spaces that are included on wiki, it seems that the origin itself could be called a vector space. I think...
Asked on 11/26/2020 by financial_physician
1 answerLet $f_n(x)$ be a series of continuous function on $[a,b]$. If $f_n(x)$ uniformly converge to a positive function, then $dfrac{1}{f_n(x)}rightrightarrowsdfrac{1}{f(x)}$. The question is rather simple and...
Asked on 11/26/2020 by user823011
2 answerI am trying to understand the solution of the following exercise:A number $a$ is unipotent if $aneq1$ and $a^2equiv 1 pmod{p}$.Show that when $p$ is prime,...
Asked on 11/25/2020 by Billy Rubina
1 answerFind for which values of $n in mathbb{N}$ it holds that $$n < e^{6 sqrt{n}}.$$I tried to use the inequality $(1 + x) leq e^x$, but from...
Asked on 11/24/2020
3 answerHow can I evaluate this integral $$int (x^2-1)(x^3-3x)^{4/3} mathop{dx}=;;?$$ My attempt: I tried using substitution $x=sectheta$, $dx=sectheta tantheta dtheta$, $$int (sec^2theta-1)(sec^3theta-3sectheta)^{4/3} sectheta tantheta dtheta...
Asked on 11/24/2020 by user801303
3 answerFind all pairs of integers $(x, y)$ such that $$x^3+y^3=(x+y)^2.$$Since $x^3+y^3 = (x+y)(x^2-xy+y^2)$ we get that $$x^2-xy+y^2=x+y$$ this can be expressed as $$x^2-(y-1)x+y^2-y=0.$$ Since we...
Asked on 11/23/2020
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