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Limit of Function Mathematic
Limits are a mathematical concept used to determine the behavior of a function as the input values get closer to a certain value. They allow analysis of what happens to a function as it approaches a particular value of the variable. Weierstrass formally introduced the concept of limits in the early 19th century by defining the limit notation, although others like Newton and Leibniz had earlier conceived of limiting processes. Examples show how to calculate specific limits, and when the limit results in an indeterminate form of 0/0, derivatives can be used to determine the limit through simplification and applying limit rules.
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Limit of Function Mathematic
- 1. Limit of afunction Erbil Technology College > Information Technology Prepared By Muhammad Kanhan Mathematic
- 2. List Of Contents Whatis importance of limits Limits allow us to think about what happens Definition Of Limit mathematical concept based on the idea of closeness Who invented Limits that thing you write as lim→ was invented by Weierstrass Some Examples Of Limits Some Basic Examples Of Limits and solution of them Fix Limits By Using Derivatives For Example if the limit equal to f(x) = 0 0 01 02 03 04 05
- 3. Definition Of Limit ALimit is the Idea of looking at what happen to a function as you approach particular value of X. Left Hand and right hand Limits are the idea of looking at what happens to a function as you approach a particular value of X From the particular direction. lim 𝑥→2 𝒇 𝑥 = 𝑥2 − 𝒙 + 𝟐 lim 𝒙→𝟐 𝒇 𝒙 = 𝟐𝟐 − 𝟐 + 𝟐 lim 𝒙→𝟐 𝒇(𝒙) = 4
- 4. Who invented Limits thatthing we write as lim→ was invented by Weierstrass, as did some others at the same time This was all in the early 19th century. Before that, in the late 17th century, both Newton and Leibniz had a conception of limiting process, which is the core notion of a limit. Neither of them gave it any sort of formalization the way Weierstrass did.
- 5. Some Examples OfLimits Example 1:-Solve for the limit of function F(x)=lim 𝑥→3 𝑥+2 𝑥 lim 𝑥→3 f(x)= 5 3 Example 2:-Solve for the limit of function F(x)=lim 𝑥→2 𝑥3+𝑥−1 𝑥+3 lim 𝑥→2 f(x)= √9 5 lim 𝑥→2 f(x)= 3 5
- 6. Some Examples OfLimits Example 3:-Solve for the limit of function F(x)=𝐥𝐢𝐦 𝒙→𝟏 𝟓+𝒙 𝟖+𝒙 𝟐+𝒙 𝐥𝐢𝐦 𝒙→𝟏 𝐟(x)= 𝟓+𝟏 𝟖+𝟏 𝟐+𝟏 𝐥𝐢𝐦 𝒙→𝟏 𝐟(x)= 𝟓+ 𝟗 𝟑 𝐥𝐢𝐦 𝒙→𝟏 𝐟(x)= 𝟖 𝟑
- 7. Fix Limits ByUsing Derivatives 𝟎 𝟎 When you get 𝟎 𝟎 you have what is called indeterminate form and you must try other techniques to determine the limit . In this case , derivative both the numerator and denominator . then apply the limit rules to the simplified expression. lim 𝑥→2 𝒇 𝑥 = 𝟒−𝑥2 𝟐−𝒙 lim 𝑥→2 𝒇 𝑥 = 𝟎 𝟎 𝑓′ 𝑥 = −𝟐𝒙 −𝟏
- 8. Fix Limits ByUsing Derivatives 𝟎 𝟎 Example 1:-Solve for the limit of function 𝐥𝐢𝐦 𝒙→𝟑 𝒇 𝒙 = 𝟐𝟕−𝒙𝟑 𝟑−𝒙 𝒍𝒊𝒎 𝒙→𝟑 𝒇 𝒙 = 𝟎 𝟎 𝒇′ 𝒙 = −𝟑𝒙𝟐 −𝟏 𝒍𝒊𝒎 𝒙→𝟑 𝒇′(𝒙) = 𝟑(𝟑)𝟐 𝟏 𝒍𝒊𝒎 𝒙→𝟑 𝒇′(𝒙) = 𝟐𝟕 𝟏 𝒍𝒊𝒎 𝒙→𝟑 𝒇′(𝒙) = 𝟐𝟕
- 9. What is importanceof limits
- 10. Thank You is thereany questions…? Prepared By Muhammad Kanhan Supervised By mrSalar