4 questions on using partial fractions to solve indefinite integrals.

For ENG1002 - Matlab Lab 4: Differentiation, Integration, Solving Differentiation equations.

For ENG1002 - Matlab Lab 4: Differentiation, Integration, Solving Differentiation equations.

For ENG1002 - Matlab Lab 4: Differentiation, Integration, Solving Differentiation equations.

JSXGraph code based on original by Christian Lawson-Perfect

The student is asked to enter an approximation to $\sqrt{n}$, where $n$ is not a square number, to 20 decimal places.

This question is a demonstration of the high precision arithmetic in Numbas v4.

The student is asked to give the Avogadro constant in scientific form, calculate the mass of a number of moles of carbon, in grams, and then calculate the number of molecules in that mass.

This is a demonstration of the high-precision decimal arithmetic in Numbas v4.0.

No description given

A sneak peek at a really clever integration of GeoGebra with Numbas.

Integration by susbtitution, no hint given

Integration by susbtitution, no hint given

A function of the form (ax+b)/(x+c) is plotted. Student is asked to calculate the shaded area. Area is both above and below the x-axis.

Two quadratic graphs are sketched with some area beneath them shaded. Question is to determine the area of shaded regions using integration. The first graph's area is all above the $x$-axis. The second graph has some area above and some below the $x$-axis.

Question is to calculate the area bounded by a cubic and the $x$-axis. Requires finding the roots by solving a cubic equation. Calculator question

Function $f(x) = xe^{ax}$ is sketched and area shaded. Question is to determine the area under graph, exactly and (calculator) to 3 s.f. Area is above x-axis.

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.

Graphs are given with areas underneath them shaded. The student is asked to select the correct integral which calculates its area.

Q1. True/false questions about basic facts.

Q2 and Q3. Velocity-time graphs are given with areas underneath them shaded. The area of the shaded regions are given. From this, definite integrals of v ar eto be determined.

Simple counting exercise, with combinations

Given a randomised rational function select the possible ways of writing the domain of the function.

Add, subtract, multiply and divide algebraic fractions.

Add, subtract, multiply and divide algebraic fractions.

Integration by susbtitution. Use the letter C for the constant.

A graph is drawn. A student is to identify the derivative of this graph from four other graphs.

Version I. Graph is quadratic

Version II. Graph is horizontal

Version III. Graph is cubic

Version IV. Graph is sinusoidal