Search - Numbas at mathcentre.ac.uk

154 results.

Indefinite integral by substitution
Draft
Question in Bill's workspace by Bill Foster

Find $\displaystyle \int \sin(x)(a+ b\cos(x))^{m}\;dx$
Indefinite integral by substitution
Draft
Question in Bill's workspace by Bill Foster

Find $\displaystyle \int \frac{c}{\sqrt{a-bx^2}}\;dx$ . Solution involves the inverse trigonometric function $\arcsin$ .
Indefinite integral by substitution
Draft
Question in Bill's workspace by Bill Foster

Find $\displaystyle \int\frac{ax+b}{(1-x^2)^{1/2}} \;dx$ . Solution involves inverse trigonometric functions.
Indefinite integral
Draft
Question in Bill's workspace by Bill Foster

Find $\displaystyle \int ae ^ {bx}+ c\sin(dx) + px ^ {q}\;dx$ .
Leicester: Integration 3
Draft
Question in Bill's workspace by Bill Foster

Find $\displaystyle \int (ax+b)\cos(cx+d)\; dx$ and hence find $\displaystyle \int (ax+b)^2\sin(cx+d)\; dx$

Also two other questions on integrating by parts.
Hyperbolic Functions 2
Draft
Question in Bill's workspace by Bill Foster

Differentiate the following functions: $\displaystyle x ^ n \sinh(ax + b),\;\tanh(cx+d),\;\ln(\cosh(px+q))$
Hyperbolic Functions 1
Draft
Question in Bill's workspace by Bill Foster

Solve for $x$ : $a\cosh(x)+b\sinh(x)=c$ . There are two solutions for this example.
Hyperbolic Functions 3
Draft
Question in Bill's workspace by Bill Foster

Find $\displaystyle \int\cosh(ax+b)\;dx,\;\;\int x\sinh(cx+d)\;dx$
Hyperbolic Functions 4
Draft
Question in Bill's workspace by Bill Foster

Find (hyperbolic substitution):
$\displaystyle \int_{b}^{2b} \left(\frac{1}{\sqrt{a^2x^2-b^2}}\right)\;dx$
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 $(a+bx) ^ {m} \sin(nx)$
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 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

Differentiate $\displaystyle \ln((ax+b)^{m})$
Chain rule
Draft
Question in Bill's workspace by Bill Foster

Differentiate $\displaystyle e^{ax^{m} +bx^2+c}$
Chain rule
Draft
Question in Bill's workspace by Bill Foster

Differentiate

$\sqrt{a x^m+b})$
Chain rule
Draft
Question in Bill's workspace by Bill Foster

Differentiate the following functions: $\displaystyle x ^ n \sinh(ax + b),\;\tanh(cx+d),\;\ln(\cosh(px+q))$
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. (Video).
Draft
Question in Bill's workspace by Bill Foster

Differentiate $\displaystyle \cos(e^{ax}+bx^2+c)$ .

Contains a video solving a similar example.
Use canvas to draw a rectangle
Ready to use
Question in How-tos by Christian Lawson-Perfect

The custom function rectangle(width,height) draws a rectangle with the given dimensions, along with some labels.
Binomial (practice of formula)
Ready to use
Question in Julie's workspace by Julie Crowley and 1 other

$X \sim \operatorname{Binomial}(n,p)$ . Find $P(X=a)$ , $P(X \leq b)$ , $E[X],\;\operatorname{Var}(X)$ .

rebelmaths
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
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 $\mu$ .
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 $t$ .
Compute Riemann sums of a linear function,
Draft
Question in Content created by Newcastle University by Newcastle University Mathematics and Statistics

Approximating integral of a linear function by Riemann sums . Includes an interactive graph in Advice showing the approximations given by the upper and lower sums and how they vary as we increase the number of intervals.

Show results for Show results for

Refine by Refine by

Status

Author

Tags

Usage rights

Ability Level

Topics