16 results authored by Katie Dexter  search across all users.

Question in Katie's workspace
Simplify fractions involving the products of factorials.

Question in Katie's workspace
$I$ compact interval, $g:I\rightarrow I,\;g(x)=ax^3+bx^2+cx+d$. Find stationary points, local and global maxima and minima of $g$ on $I$

Question in Katie's workspace
$I$ compact interval, $g:I\rightarrow I$, $g(x)=(xa)(xb)^2$. Stationary points in interval. Find local and global maxima and minima of $g$ on $I$.

Question in Katie's workspace
Linear combinations of $2 \times 2$ matrices. Three examples.

Question in Katie's workspace
Multiplication of $2 \times 2$ matrices.

Question in Katie's workspace
$I$ compact interval. $\displaystyle g: I\rightarrow I, g(x)=\frac{x^2}{(xc)^{a/b}}$. Are there stationary points and local maxima, minima? Has $g$ a global max, global min?

Question in Katie's workspace
Seven standard elementary limits of sequences.

Question in Katie's workspace
Putting a pair of linear equations into matrix notation and then solving by finding the inverse of the coefficient matrix.

Question in Katie's workspace
Find the stationary point $(p,q)$ of the function: $f(x,y)=ax^2+bxy+cy^2+dx+gy$. Calculate $f(p,q)$.

Question in Katie's workspace
Step by step solving for integration by substitution

Question in Katie's workspace
Given that $\displaystyle \int x({ax+b)^{m}} dx=\frac{1}{A}(ax+b)^{m+1}g(x)+C$ for a given integer $A$ and polynomial $g(x)$, find $g(x)$.

Question in Katie's workspace
Given that $\displaystyle \int x({ax+b)^{m}} dx=\frac{1}{A}(ax+b)^{m+1}g(x)+C$ for a given integer $A$ and polynomial $g(x)$, find $g(x)$.

Question in Katie's workspace
Find $\displaystyle \int (ax+b)\cos(cx+d)\; dx $

Question in Katie's workspace
Given $\displaystyle \int (ax+b)e^{cx}\;dx =g(x)e^{cx}+C$, find $g(x)$. Find $h(x)$, $\displaystyle \int (ax+b)^2e^{cx}\;dx =h(x)e^{cx}+C$.

Question in Katie's workspace
Solving integration by substitution without help

Question in Katie's workspace
Simplify fractions involving the products of factorials.