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Limits and continuity calculus pdf11/7/2023 x 1 Compute limit from both sides as follow x approaching 1 from left x approaching 1 from right x 0.9 0.99 0.999 0.9999 1 1.0001 1.001 1.01 1.1 f(x) 1.8 1.98 1.998 1.9998 ? 2.0002 2.002 2.062 2.1 lim 2 x 2 x 1 lim 2 x 2 x 1 Since limit from left and right (one sided limit) exist and equal, two side limit exist and written as lim 2 x 2 x 1 Example Evaluate lim x 0 sin x x numerically where x is in radian. By doing so, we are expecting to reach a certain value LIMIT Aim: to be able to interpret limit behavior based on looking at a table of values Example Evaluate lim 2 x by using table. 1 Numerical Evaluating Limit 3 Analytical 2 Graphical Numerical Method In this method, limit is solved by inserting an appropriate value of x from left (left side limit) and right (right side limit) and calculate the corresponding f(x). LIMIT Limit can be evaluated using three methods. x approaches c from right x approaches c from left Limit exist because one sided limit exist and the value are equal. Definition – Limit: If the limit from the left and right sides have the same value, lim f ( x) lim f ( x) L x c x c f ( x) exist and it is written as Then, lim x c lim f ( x) L x c and we read as “the limit f x as x approaches c is L ”. 1.1 Limit of a Function When does a limit EXIST? A limit exists if and only if both corresponding one sided limits exist and are equal. The notation of one sided limit is given as follow lim f x lim f x L x c x c Left Side Limit Right Side Limit x approaches c from left. In limit, we are not interested in the value of f(x) when x = c We are more interested in the behaviour of f(x) as x comes closer and closer to a value of c. x 0, but yet as you get close and close to the fire you have sense that temperature on the surface of your body will increasing until it reaches the temperature of fire. Now you would not want to actually put yourself in the fire i.e. The closer you get, the greater the sense of heat. Now as you getting closer to the fire, increased heat are felt on your body. Let the temperature on the surface of your body measured as f ( x). As you keep on moving, you start feel heat all over your body. Imagine that you are moving closer to the forest, the distance x between you and forest is decreases. Suppose there is a huge forest blaze with a raging fire. Consider an example which will help you to understand the concept of limit. The concept of limit study what will happen to a function when variable x approaches a certain value. All you need is to develop an intuitive understanding, and you will see how simple these concepts are. The main ideas of calculus, the derivative and the integral, are defined using limits. Continuity 1.1 Limit of a Function Limit is the most important concept of all calculus. Limit at Infinity 3.Evaluate Limit : Graphical Method 6. Siti Zanariah Satari, Mohd Nizam Kahar, Norazaliza Mohd Jamil, Calculus for Science & Engineering, First Edition UMP Contents 1. The First Course of Calculus for Science & Engineering Students, Second Edition. Abdul Wahid Md Raji, Hamisan Rahmat, Ismail Kamis, Mohd Nor Mohamad, Ong Chee Tiong. Students should be able to determine continuity at a given point by referring to continuity test References 1. Students should be able to explain the continuity test 2. Students should be able to compute the limit at infinity Description Expected Outcomes 1. Students should be able to find limit numerically, analytically and graphically 4. Students should be able to explain one sided limit and two sided limit 3. Students should be able to describe the concept of limits 2. determine the continuity of the function Expected Outcomes 1. evaluate limit using three different approaches. explain the definition of one sided and two sided limit 3. \)” If a function is continuous at every point in its domain, we simply say the function is “continuous.” Thus, continuous functions are particularly nice: to evaluate the limit of a continuous function at a point, all we need to do is evaluate the function.Calculus Chapter 1 Limit & Continuity Norhafizah Md Sarif Faculty of Industrial Sciences & Technology Description Aims This chapter is aimed to : 1.
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