Or search by topic

There are **20** NRICH Mathematical resources connected to **Limits**, you may find related items under Calculus.

Problem
Primary curriculum
Secondary curriculum
### Spokes

Draw three equal line segments in a unit circle to divide the circle into four parts of equal area.

Age 16 to 18

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Exponential Trend

Find all the turning points of y=x^{1/x} for x>0 and decide whether each is a maximum or minimum. Give a sketch of the graph.

Age 16 to 18

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Discrete Trends

Find the maximum value of n to the power 1/n and prove that it is a maximum.

Age 16 to 18

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Witch of Agnesi

Sketch the members of the family of graphs given by y = a^3/(x^2+a^2) for a=1, 2 and 3.

Age 16 to 18

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### There's a Limit

Explore the continued fraction: 2+3/(2+3/(2+3/2+...)) What do you notice when successive terms are taken? What happens to the terms if the fraction goes on indefinitely?

Age 14 to 18

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Rain or Shine

Predict future weather using the probability that tomorrow is wet given today is wet and the probability that tomorrow is wet given that today is dry.

Age 16 to 18

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Converging Product

In the limit you get the sum of an infinite geometric series. What about an infinite product (1+x)(1+x^2)(1+x^4)... ?

Age 16 to 18

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Over the Pole

Two places are diametrically opposite each other on the same line of latitude. Compare the distances between them travelling along the line of latitude and travelling over the nearest pole.

Age 16 to 18

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Production Equation

Each week a company produces X units and sells p per cent of its stock. How should the company plan its warehouse space?

Age 16 to 18

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Resistance

Find the equation from which to calculate the resistance of an infinite network of resistances.

Age 16 to 18

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Squareflake

A finite area inside and infinite skin! You can paint the interior of this fractal with a small tin of paint but you could never get enough paint to paint the edge.

Age 16 to 18

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Golden Fractions

Find the link between a sequence of continued fractions and the ratio of succesive Fibonacci numbers.

Age 16 to 18

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Golden Eggs

Find a connection between the shape of a special ellipse and an infinite string of nested square roots.

Age 16 to 18

Challenge Level

Article
Primary curriculum
Secondary curriculum
### Fractional Calculus III

Fractional calculus is a generalisation of ordinary calculus where you can differentiate n times when n is not a whole number.

Age 16 to 18

Article
Primary curriculum
Secondary curriculum
### Fractional Calculus II

Here explore some ideas of how the definitions and methods of calculus change if you integrate or differentiate n times when n is not a whole number.

Age 16 to 18

Article
Primary curriculum
Secondary curriculum
### Fractional Calculus I

You can differentiate and integrate n times but what if n is not a whole number? This generalisation of calculus was introduced and discussed on askNRICH by some school students.

Age 16 to 18

Problem
Primary curriculum
Secondary curriculum
### Squaring the Circle and Circling the Square

If you continue the pattern, can you predict what each of the following areas will be? Try to explain your prediction.

Age 14 to 16

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Lower Bound

What would you get if you continued this sequence of fraction sums? 1/2 + 2/1 = 2/3 + 3/2 = 3/4 + 4/3 =

Age 14 to 16

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Reciprocal Triangles

Prove that the sum of the reciprocals of the first n triangular numbers gets closer and closer to 2 as n grows.

Age 16 to 18

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Triangle Incircle Iteration

Keep constructing triangles in the incircle of the previous triangle. What happens?

Age 14 to 16

Challenge Level