# Tagged Questions

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### Getting “semi” orthogonal basis from a linear independent set

Let $K_i: \mathbb{R}\mapsto \mathbb{R}^k$ are continuous functions for all $i=1,\dots,k-d$ such that for every fixed $t\in\mathbb{R}$ we have ${\cal K}_t=\{K_1(t),\dots,K_{k-d}(t)\}$ be a linear ...
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### $g''(t_0)$ where $g(t) = f(t, 1-t) , t_0 = 0$

Let z = f(x,y) be a differentiable function such that $\frac{∂f}{∂x}$ (0,1) = -1 ,$\frac{∂f}{∂y}$ (0,1) = 2 , $\frac{∂^2f}{∂x^2}$ (0,1) = 2 , $\frac{∂^2f}{∂x∂y}$ (0,1) = -1 , $\frac{∂^2f}{∂y^2}$ ...
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### The Derivative of a General Linear Map

This question is somewhat abstract compared to the things we've discussed in class, so I'm just making sure I've got the right idea. I'd appreciate any help/suggestions; I'm pretty sure I've got the ...
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### Equation of plane that goes for intersection of 2 planes and is perpindicular to another plane

Really don't know what to do here, went to a tutor neither did he. Okay first the problem: Find the equation of the plane that passes through the line of intersection of the planes x − z = 2 and y + ...
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### Multivariable Calculus Vector Fields

I have to prove that if $f(x,y,z)=f_{a}(x,y,z)+f_b(x,y,z)+f_c(x,y,z)$ is a conservative vector field and and $g(x,y,z)=g_{a}(x,y,z)+g_b(x,y,z)+g_c(x,y,z)$ is also a conservative vector field, then ...
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### Solving resulant vectors without plotted points 2 axis graph

Not putting precise problem in here because I'm just looking for guidance. Basically I have two vectors who are given magnitudes in Pounds, and I have to find the magnitude and angle (with respect to ...
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### transforming a vector from cartesian to spherical and cylindrical co-ordinate system

I know the formula(which i don't know how to copy here but it was in matrix form) for transforming a vector from cartesian system to spherical or cylindrical coordinate system. But, I want to know its ...
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### Vector calculus: Finding a model fit from a 2D grid

First of all, I am a biologist. My knowledge of math is very limited. Therefore, I come here for help, but please take into consideration that I may not be very good at asking the question in a good ...
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### Do the paths intersects? If so where

There are two unidentified objects in the sky. The path of the first object is given by $r(t)=\langle t,-t,1-t\rangle$ and the second object's path is $s(t)= \langle t-3,2t,4t\rangle$ Do the paths ...
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### How to prove that $f(x,y)=\sqrt{x^2+y^2}$ is continuous in $\mathbb{R}^2$? [duplicate]

Please, I need the demonstration (step by step) of the continuity in $\mathbb{R}^2$ of the function $f(x,y)=\sqrt{x^2+y^2}$. I know that the function is continuous in $\mathbb{R}^2$, but I just don´t ...
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