Find the matrix associated with the linear map $f:R^2 \rightarrow R^2$ defined by $f(x,y)=(3x-y,y-x)$ with respect to the ordered basis ${(1,0),(1,1)}$ Le...

Can someone help me understand how to calculate the limit: $\lim_{n \to \infty} n [\sqrt{n+4}-\sqrt{n} ] $ ? How can I det rid the floor function ?! (Mult...

For the function $f(x) = x^{1/3}$ on the interval $[1,8]$ find the point $(c,f(c))$ guaranteed by the Mean Value Theorem, at which the slope of the tangen...

I have the following... $$z=\sqrt{x^2+y^2}$$ I need to write this as an equation in spherical coordinates. I know that $p^2 = x^2+y^2+z^2$ and that... $$x...

I'm reading the book Mathematics: It's Content, Methods, and Meanings and I'm unsure as to how one of the variables in an example was deriv...

What would $2^{3^4}$ equate to? I can think of two rules that may apply: $a^{b^c} = a^{(b^c)}$ (Making $2^{3^4} = 2^{81}\approx2.417\cdot10^{24}$) or $a^{...

What exactly does 'linear' mean. For example, Hilbert space is a linear space. What is the difference between a linear and a 'non-linear�...

An airplane passes over an airport at noon traveling $540$ mi/hr due north. At 1:00pm, another airplane passes over the same airport at the same elevation...

Looking at a simple algebra question which is to graph "All numbers that are less than four units from zero." The knee jerk response is to draw ...

Given the function $h(x,y,z)=5+x^2-3yz$ represents the temperature. find the directional derivative on the point $P(1,2,-1)$ that does the same angles in ...