Limit theorem.
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The document is a presentation on the concept of limit theorem by Prof. Sadiq Hussain Manjanbazam, aimed at students with prior knowledge in trigonometry and geometry. It covers essential topics such as the area of triangles, the sandwich theorem, and the properties of limits in trigonometric functions. The lesson includes examples, class practices, and a recap session, highlighting the importance of the limit theorem in calculus.
Limit theorem.
- 2. CONCEPT LIMIT THEOREM By Prof. SADIQ HUSSAIN Manjanbazam Cadet College Ghazi,TarbelaCantt. Presentation on concept Delivery
- 3. PRIOR KNOWLEDGE Student should have knowledge of the concept of the trigonometry. Area of a sector of a circle. Rule of finding area of a triangle when its two sides and its included angle is known. Area of a right-angled triangle when its angle and adjacent side is known. Basic rules of in-equalities. Basic concept of limit of a trigonometric function.
- 4. Ojectives of the lesson. Student will be able to understand: The concept of lmit theorem. The concept of limit of trigonometic Functions,i.e.
- 5. THE AIM To teach the student ‘The Sand-witch Theorem’ 0 sin lim 1 θ θ θ→ =
- 6. INTRODUCTION Some examples will be shown the class: Area of a triangle when its two sides & its included angle is given. What is area of triangle?. For area of different triangle two sides and included angle play video Area of a Triangle - 2 Sides & Included Angle.webm
- 7. INTRODUCTION…contd Q. Student will be asked to find area of a sector? For finding the area of a sector play this video plz How do we Find the Area of a Sector- - YouTube.mkv
- 9. INTRODUCTION…contd Students will be shown real picture of sandwich
- 10. THE LESSON AIM Now the aim of the lesson will be announced, Student today we will study . concept of ‘The sandwich Theorem’.
- 11. To prove the sine limit
- 12. DEVELOPMENT Let f.g and h be functions such that,f(x)≤g(x)≤h(x).
- 13. DEVELOPMENT …contd Hence the required result. Remark; In this result ‘angle will be measured in radian’ 0 sin lim 1 θ θ θ→ =
- 14. Explanation of limit properties.
- 15. Examples.
- 16. Contd……..
- 17. Contd…..
- 18. Examples for class practice.
- 19. Recapitulation An oral recap will be carried in about three minutes which will cover the following points’; Students will be asked about an difficulty if they have any. Students will be asked why ‘LIMIT THEOREM’ is important in calculus. Why sand-witch theorem is needed in Limit Theorem.
- 20. Homework Q.1 Evaluate the following.
- 21. THANK YOU