Finding Gradients of Curves
Introduction
I am going to investigate the gradients of different curves and try to
work out a pattern that I could use to find the gradient of any curve.
I will draw graphs of a selection of curves, some by hand, some using
Autograph and some using Excel. I will use three methods to
investigate the graphs. Firstly, I will draw tangents to the curves at
4 or 5 points and measure the gradients. Secondly, I will draw chords
between x = 1 and 4 or 5 points and measure the gradients. Thirdly, I
will use algebra to work out a formula for the gradient and see how
this matches the first two methods.
At first I split up the coursework into 3 main families (for each
family there are additional equations to investigate):
Part One: Curves involving x2
1. y = x2
2. y = 2x2
3. y = 3x2
4. y = 4x2
5. y = x2 + 1
6. y = 7x2 + 6
Part Two: Curves involving x2 + x
1. y = x2 + x
2. y = x2 + 2x
3. y = 7x2 + 4x + 5
Part Three: Curves involving x3 + x
1. y = x3
2. y = 2x3
3. y = 4x3 + 2x - 5
Finally, I will summarise my results in a series of tables and work
out an overall formula that I could use to predict the gradient of any
curve.
PART ONE: CURVES CONTAINING X2
(1) y = x2
I am investigating the changes in gradient for the curve y = x2. To
plot the curve, I will use the table of values given below.
x
0
1
2
3
4
5
6
y
0
1
4
9
16
25
on the y. If my prediction is right I should be able to draw a
I have plotted graphs from both sets of calculated gradients however I will concentrate on the graph plotted from the results show above as
James is a man nearing forty. His build is average; he has light skin and dark hair. He is sensible and caring enough for his partners. He’s dismayed that Nolan has been killed. They were close friends in the office.
Read the initial buret readings for both burets to the nearest 0.01 ml. Use a buret reading card to make the meniscus more prominent. Record readings on the report sheet. Have your instructor check and initial your report sheet for your first buret reading (sample #1, only). 6. Rinse a clean 125 ml Erlenmeyer flask with deionized water. Deliver approximately 20 ml of unknown acid into the Erlenmeyer flask. The tip of the buret should be approximately 1/2 inch below the top of the flask to avoid loss due to splashing. 7. Add 2 or 3 drop of phenolphthalein indicator. (Above your lab bench). 8. Titrate the unknown acid by adding standard NaOH (from the buret). Swirl the flask to mix the solutions during the addition of base. As the base is added you will observe a pink color localized at the spot the NaOH enters the solution (this is due to a localized high base concentration). Occasionally, rinse down the walls of your flask with deionized water (This rinses down any acid that has splashed onto the walls of your flask). Near the end-point, the pink color "flashes" throughout the solution and remains for a slightly longer time (1-2 seconds). When this occurs, add the NaOH drop by drop and eventually half-drops until the pink color remains (for at least 30 seconds). This is the end-point! NOTE: If you over-shoot the end-point (too much NaOH is added), add 1-2 more ml of the Unknown acid and then add NaOH again until a proper end-point is reached. Be sure
Write a differential in this case and explain how each item in your differential fits and how it might not fit.
Then take the ruler and put it on the end of the opisthocranion and measure the distance in cm,record your answer on the table
slope. I think that out of all the variables, this is the one which is
A titration curve is a plot of pH of the analyte solution versus volume of titrant added, as the titration progresses. 9,12 The equivalence point is the inflection point of a titration curve.9
Living in a divided society based upon the religions of the Puritans and the Quakers, Evan Feversham sought out his own religious faith through his daily interactions with both religious groups.
The Canny edge detection algorithm is commonly known as the optimal edge detector. During his research work, Canny's main intentions were to enhance the edge detectors which were already out at that time. Canny was successful in his objective and published a paper entitled "A Computational Approach to Edge Detection" in which he mentions a list of criteria which could improve current methods of edge detection. According to him, low error rate was one of the important criteria. Secondly, the edges in the image must not be missed and there must be no response to non-edges. Thirdly, the edge points must be well localized that is the distance between the edge pixels found by the detector and the actual edge must be minimum. And lastly, only one response
Refraction of Light Aim: To find a relationship between the angles of incidence and the angles of refraction by obtaining a set of readings for the angles of incidence and refraction as a light ray passes from air into perspex. Introduction: Refraction is the bending of a wave when it enters a medium where it's speed is different. The refraction of light when it passes from a fast medium to a slow medium bends the light ray toward the normal to the boundary between the two media. The amount of bending depends on the indices of refraction of the two media and is described quantitatively by Snell's Law. (Refer to diagram below)
The specimen must be regularly shaped in the form of a wire; its diameter. should be measured at six different points. Variables and Controls:. The variables that I will be using are the length and diameter of the
Then use the information in the text book to create a bar graph on the website above.
-In order to solve this differential equation you look at it till a solution occurs to you.
A French curve is a template made out of metal, wood or plastic composed of many different curves. It is used in manual drafting to draw smooth curves of varying radii. The curve is placed on the drawing material, and a pencil/knife is traced around its curves to produce the desired result. In garment design they are mainly used for pattern drafting, pattern alteration