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115 results.

Product rule
Draft
Question in Bill's workspace by Bill Foster

Differentiate $\sin(ax+b) e ^ {nx}$ .
Product rule
Draft
Question in Bill's workspace by Bill Foster

Differentiate $x^m\cos(ax+b)$
Product Rule
Draft
Question in Bill's workspace by Bill Foster

Differentiate the function $f(x)=(a + b x)^m e ^ {n x}$ using the product rule. Find $g(x)$ such that $f\;'(x)= (a + b x)^{m-1} e ^ {n x}g(x)$ .
Product rule
Draft
Question in Bill's workspace by Bill Foster

Differentiate the function $(a + b x)^m e ^ {n x}$ using the product rule.
Chain rule
Draft
Question in Bill's workspace by Bill Foster

The derivative of $\displaystyle x ^ {m}(ax^2+b)^{n}$ is of the form $\displaystyle x^{m-1}(ax^2+b)^{n-1}g(x)$ . Find $g(x)$ .
Chain rule
Draft
Question in Bill's workspace by Bill Foster

Differentiate the following functions: $\displaystyle x ^ n \sinh(ax + b),\;\tanh(cx+d),\;\ln(\cosh(px+q))$
Interactive Newton-Raphson method
Should not be used
Question in Christian's workspace by Christian Lawson-Perfect and 1 other

Write down the Newton-Raphson formula for finding a numerical solution to the equation $e^{mx}+bx-a=0$ . If $x_0=1$ find $x_1$ .

Included in the Advice of this question are:

6 iterations of the method.

Graph of the NR process using jsxgraph. Also user interaction allowing change of starting value and its effect on the process.
Find partial derivatives of $f(x,y)$ and identify its stationary points
Has some problems
Question in Content created by Newcastle University by Christian Lawson-Perfect and 1 other

Find the stationary points of the function: $f(x,y)=a x ^ 3 + b x ^ 2 y + c y ^ 2 x + dy$ by choosing from a list of points.

Inputting the values given into the partial derivatives to see if 0 is obtained is tedious! Could ask for the factorisation of equation 1 as the solution uses this. However there is a problem in asking for the input of the stationary points - order of input and also giving that there is two stationary points.
Prove discontinuity of a function at a given point
Ready to use
Question in Content created by Newcastle University by Newcastle University Mathematics and Statistics

A graphical approach to aiding students in writing down a formal proof of discontinuity of a function at a given point.

Uses JSXgraph to sketch the graphs and involves some interaction/experimentation by students in finding appropriate intervals.
True/false statements about continuity at a point
Has some problems
Question in Content created by Newcastle University by Newcastle University Mathematics and Statistics and 1 other

No description given
20122013 CBA0_4
Has some problems
Question in Content created by Newcastle University by Newcastle University Mathematics and Statistics

Given a discrete random variable $X$ find the expectation of $1/X$ and $e^X$ .
Log-likelihood and maximum likelihood estimator for PDF
Ready to use
Question in Content created by Newcastle University by Newcastle University Mathematics and Statistics

Given a PDF $f(x)$ on the real line with unknown parameter $t$ and three random observations, find log-likelihood and MLE $\hat{t}$ for $t$ .
Find maximum likelihood estimator of mean of normal distribution
Ready to use
Question in Content created by Newcastle University by Newcastle University Mathematics and Statistics

Given sum of sample from a Normal distribution with unknown mean $\mu$ and known variance $\sigma^2$ . Find MLE of $\mu$ and one of four functions of $\mu$ .
Find $\mu(n)$ , $\sigma(n)$ , $\tau(n)$ , $\phi(n)$
Draft
Question in Content created by Newcastle University by Newcastle University Mathematics and Statistics

Number Theory.

Given $n \in \mathbb{N}$ find $\mu(n),\;\tau(n),\;\sigma(n),\;\phi(n).$
Construct a probability distribution function, then find CDF and expectation
Draft
Question in Content created by Newcastle University by Newcastle University Mathematics and Statistics

The random variable $X$ has a PDF which involves a parameter $c$ . Find the value of $c$ . Find the distribution function $F_X(x)$ and $P(a \lt X \lt b)$ .

Also find the expectation $\displaystyle \operatorname{E}[X]=\int_{-\infty}^{\infty}xf_X(x)\;dx$ .
Maclaurin series (three terms)
Draft
Question in Content created by Newcastle University by Newcastle University Mathematics and Statistics

Find the first 3 terms in the MacLaurin series for $f(x)=(a+bx)^{1/n}$ i.e. up to and including terms in $x^2$ .
Integrate algebraic fraction
Draft
Question in Content created by Newcastle University by Newcastle University Mathematics and Statistics

Find $\displaystyle \int\frac{ax^3+ax+b}{1+x^2}\;dx$ . Enter the constant of integration as $C$ .
Integral by hyperbolic substitution
Draft
Question in Content created by Newcastle University by Newcastle University Mathematics and Statistics

Find (hyperbolic substitution):
$\displaystyle \int_{b}^{2b} \left(\frac{1}{\sqrt{a^2x^2-b^2}}\right)\;dx$
Calculate definite integral with a hyperbolic substitution
Draft
Question in Content created by Newcastle University by Newcastle University Mathematics and Statistics

Find (hyperbolic substitution):
$\displaystyle \int_{b}^{2b} \left(\frac{1}{\sqrt{a^2x^2-b^2}}\right)\;dx$
Indefinite integral by substitution
Draft
Question in Content created by Newcastle University by Newcastle University Mathematics and Statistics

Find $\displaystyle \int \sin(x)(a+ b\cos(x))^{m}\;dx$
Definite integration using standard integrals
Draft
Question in Content created by Newcastle University by Newcastle University Mathematics and Statistics

Calculate definite integrals: $\int_0^\infty\;e^{-ax}\,dx$ , $\int_1^2\;\frac{1}{x^{b}}\,dx$ , $\; \int_0^{\pi}\;\cos\left(\frac{x}{2n}\right)\,dx$
Integration: Indefinite integral
Draft
Question in Content created by Newcastle University by Newcastle University Mathematics and Statistics

Find $\displaystyle \int ae ^ {bx}+ c\sin(dx) + px ^ {q}\;dx$ .
Integration by parts
Draft
Question in Content created by Newcastle University by Newcastle University Mathematics and Statistics

Find $\displaystyle \int (ax+b)\cos(cx+d)\; dx$ and hence find $\displaystyle \int (ax+b)^2\sin(cx+d)\; dx$
Indefinite integration using standard integrals
Draft
Question in Content created by Newcastle University by Newcastle University Mathematics and Statistics

Integrate $f(x) = ae ^ {bx} + c\sin(dx) + px^q$ . Must input $C$ as the constant of integration.
Integral of improper polynomial fraction
Draft
Question in Content created by Newcastle University by Newcastle University Mathematics and Statistics

Find $\displaystyle \int \frac{nx^3+mx^2+nx + p}{1+x^2}\;dx$ . Solution involves $\arctan$ .
Indefinite integral of improper polynomial fraction
Draft
Question in Content created by Newcastle University by Newcastle University Mathematics and Statistics

Find $\displaystyle \int \frac{nx^3+mx^2+nx + p}{1+x^2}\;dx$ . Solution involves $\arctan$ .
Indefinite integral by substitution
Draft
Question in Content created by Newcastle University by Newcastle University Mathematics and Statistics

Find $\displaystyle \int \frac{c}{\sqrt{a-bx^2}}\;dx$ . Solution involves the inverse trigonometric function $\arcsin$ .
Integral of improper polynomial fraction
Draft
Question in Content created by Newcastle University by Newcastle University Mathematics and Statistics

Find $\displaystyle \int\frac{ax^3+ax+b}{1+x^2}\;dx$ . Enter the constant of integration as $C$ .
How to enter functions - Getting Started
Ready to use
Question in Content created by Newcastle University by Newcastle University Mathematics and Statistics and 1 other

Dealing with functions in Numbas.
Integration by parts
Draft
Question in Content created by Newcastle University by Newcastle University Mathematics and Statistics

Find $\displaystyle \int x\sin(cx+d)\;dx,\;\;\int x\cos(cx+d)\;dx$ and hence $\displaystyle \int ax\sin(cx+d)+bx\cos(cx+d)\;dx$

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