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For the function f(x) = 4x. Find lim(x t...

For the function `f(x) = 4x`. Find `lim_(x to 2) f (x)`

Text Solution

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Let us compute the value of function for values of x very near to 2.
Firstly, we consider values of x approaching 2 from the left i.e., `x lt 2`
`{:(x,1.5,1.6,1.7,1.8,.1.9,1.99,1.999),(f(x)=4x,6,6.4,6.8,7.2,7.6,7.96,7.996):}`
Now, we consider values of x approaching 2 from the right i.e., `x gt 2`
`{:(x,2.3,2.2,2.1,2.05,2.03,2.01,2.001),(f(x)=4x,9.2,8.8,8.4,8.2,8.12,8.04.8.004):}`
Now from both the tables we observe that x approaches 2 either from left or right, the value of f(x) seems to approach 8.
So, `underset(x to 2)(lim) f(x) = underset(x to 2^(+))(lim) f(x) = underset(x to 2)(lim) f(x) = 8`
This can be shown by the graph also

Here, again the value of the function at x = 2 coincide with the limit at x = 2
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