Differential Calculus and Trigonometry (Revision and problems)

mezoelprince · #1 09-06-2008, 07:52 PM

مفاجأة لكل اللي بياخدو ماس بالإنجليش .....
أنا حاولت ألأخص على قد ما أقدر منهج ال calculus وال trig

بعدين هبقى أحط مسائل بالتدريج من الصعب للسهل ......

و إنشاء الله تعجبكم .....

ولو حد عايز أي حاجة أشرحهاله أوضحاله .. أنا موجوووووووووووووووووووووووووووووود

مش مستنيين بقى غير إنكو تدعوا إن ربنا يوفقني و يديني اللي نفسي في إنشاء الله ....
(في المرفقات ملف وورد)

mezoelprince · #2 09-06-2008, 08:10 PM

هنبدأ الأول بمسائل ال Trig(sum and difference between angles) ......

1) Without using the calculator find:

2)Without using the calculator find

3)without using caculator find

4)Find:
4)

5) Prove that:

6) Without using the calculator prove that:

mezoelprince · #3 09-06-2008, 08:18 PM

بعدين مسائل (Double Angles)

1)Find:

2)Find:
http://www.aladwaa.com/QBImg/MTE11/MTE111442.gif

3) Simplify:

http://www.aladwaa.com/QBImg/MTE11/MTE111451.gif

4) Simplify:

5) Prove that:

http://www.aladwaa.com/QBImg/MTE11/MTE111473.gif

mezoelprince · #4 09-06-2008, 08:23 PM

نخش بقى على ال Limits

1)Find:

2)find:

3)Find:

4)Find:

5)Find:

mezoelprince · #5 09-06-2008, 08:26 PM

نشد بقى على ال Differentiation and first derivative

1)Find the slope of the tangent to the curve of f(x) = 8x2 + 1 at each of the following points

2)A cube expands regularly such that it preserves its shape. Find the average rate of change in its total faces area as its edge length changes from 20 cm to 20.4 cm. Then calculate the rate of change of the volume of the cube when its edge length is 20 cm.

3)The length of a rectangular lamina is three times its width. The lamina expands such that it preserves its shape with the same ratio between its dimensions. Find the rate of change of its area when its width is 20 cm.

4)Find the rate of change of the function

mezoelprince · #6 09-06-2008, 08:31 PM

نديها بقى elevation and depression و كمان solution of the triangle

1)From a window of a building 8 m high, the elevation angle of the top of a tree was measured and found to be 25 , and the measure of the depression angle of the bottom of such tree was 40 . Find the height of the tree and its distance from the building.

2)A man observed the top of a tower at an angle of elevation of 25 . When he walked horizontally towards the base of the tower 40 meteres, the measure of the anlge of elevation of the top became 42 . Find the height of the tower.

3)A ship started sailing in the direction 18 south west with velocity 25 km/h. At the same time another ship started sailing from the same point in the direction 48 west north with velcoity 15 km/h. find the distance between the two ships after two hours.

4)A tree was broken such that its top touched the ground and its upper part made an angle of measure 50 with the ground. If the top of the tree was at distance 8 m from its bottom. Find the length of the tree.

5)ABCD is a parallelogram, AB = 32 cm, BC = 44 cm, BD = 36 cm. Find:
i) AC
ii) area of parallelogram ABCD.

6) Solve the triangle with a = 1.25 cm, b = 2.05 cm, c = 1.52 cm.