# Download Calculus: How Calculus Works (Studymates in Focus) by Christine Tootill PDF

By Christine Tootill

Who else are looking to succeed in arithmetic? Calculus frequently factors panic in scholars, yet with this booklet, that quickly could be a factor of the prior. filled with transparent causes and written by way of a hugely skilled and sympathetic instructor with decades of expertise in getting ready scholars for complicated arithmetic examinations, it is a convinced must-have ebook for all scholars learning arithmetic.

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Extra resources for Calculus: How Calculus Works (Studymates in Focus) (In-Focus)

Example text

3. The line y = −3x is a normal to the curve y = k − x2 at the point N. (i) Find the co-ordinates of N. (ii) Find the value of k. (iii) Find the equation of the tangent to the curve at N. Practical assignment (9) Use your graphics calculator to find the co-ordinates of the point where the normal to the curve y = x2 at the point (1,1) intersects with the curve in the 2nd quadrant. Alternatively, find the equation of the normal, form a quadratic equation, solve it for x and lastly find the y co-ordinate.

In higher mathematics, there are methods of differentiation for functions of more than one variable. These methods are needed when the variables are independent. indb 44 1/22/2008 1:01:06 PM How to apply the theory Tutorial Progress questions (8) Complete the drinks can problem as follows: a) Find the height of the can and the area of the aluminium when the radius was 3 cm. 4 cm. 4 cm. Practical assignment (8) An open-topped water tank with a square base has a capacity of 4000 litres. Find the height and the width of the tank.

State the co-ordinates of each stationary point and use the method shown in this chapter to establish which is a maximum and which is a minimum. Use your results to sketch the curve. Practical assignment (7) Cut out a rectangular piece of card measuring 20 cm by 12 cm. Cut out a square from each corner measuring 1 cm by 1 cm. Fold the edges of the card up to make a box without a lid. Calculate the volume of the box in cm3. Then calculate what the volume of the box would be if you had cut off corners measuring 2 cm by 2 cm.