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Finding Limits NumericallyFinding limits numerically which means we have to consider approximately some values of x which are closer to the given number from left and right side. And check for which value of x we are getting the function undefined. We can check this by graphing also.Steps for sketching the graph Step 1 : Find the xintercepts of the given function. Step 2 : Find the yintercept of the given function. Step 3 : Mark if there is any vertical or horizontal asymptotes if any. Step 4 : Get some xvalues, plug in that values in the given function and find the y values. (Make a function table). Examples on Finding Limits NumericallyExample 1 : Sketch the graph of the function$f(x) = \frac{x^{3}1}{x1}$ Solution : First we will graph the given function using curve sketching technique explained above. As the denominator contains x1, so we get confused what to do when x=1. So to get an idea about the behavior of the graph near to x= 1. We will use the two set of values of x, one set of values from left side approaches to 1 and other set of values from the right side approaches to 1. The graph of the given function is a parabola but there is a gap at (1,3) as shown in the above graph. From the graph and the table will understand that x can not be equal to 1 and the f(x) or y will be close to 3. So we will write this using limit notation as $\lim_{x>1}f(x) = 3$ This can be read as " the limit of f(x), x approaches to 1 is 3" Example 2 : Estimate the limit numerically. $f(x)=\frac{x4}{x^{2}3x4}$ $ \lim_{x>4}\frac{x4}{x^{2}3x4}$ Solution : As the given limit approaches to x= 4 so we will consider some values of x from left side of 4 and some values of x from the right side of 4. x values from the left side = 3.9,3.99,3.999,4 x values from the right side = 4.001,4.01,4.1 We will plug in the above value in the given function. x= 3.9 $f(3.9)=\frac{3.94}{3.9^{2}3(3.9)4} =0.2040 $ x=3.99 $f(3.99)=\frac{3.994}{3.99^{2}3(3.99)4} =0.200400 $ x=3.999 $f(3.999)=\frac{3.9994}{3.999^{2}3(3.999)4} =0.20004000 $ x= 4 $f(4)=\frac{44}{4^{2}3(4)4} = undefined (no value)$ x= 4.001 $f(4.001)=\frac{4.0014}{4.001^{2}3(4.001)4} = 1.99960$ x= 4.01 $f(4.01)=\frac{4.014}{4.01^{2}3(4.01)4} = 1.99601$ x=4.1 $f(4.1)=\frac{4.14}{4.1^{2}3(4.1)4} = 1.996078$ From the above, we can see that when we get closer to 4 the value gets closer to 0.20. So we can conclude that $ \lim_{x>4}\frac{x4}{x^{2}3x4} \approx 0.2$ Covid19 has led the world to go through a phenomenal transition . Elearning is the future today. Stay Home , Stay Safe and keep learning!!! Covid19 has affected physical interactions between people. Don't let it affect your learning. From finding limits numerically to Home
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