Answer:
[tex]+\infty[/tex]
Step-by-step explanation:
The expression for the right hand limit of f(x) is:
[tex]f = \frac{x+\epsilon}{x + \epsilon - 5}[/tex]
The expression can be simplified with some algebraic handling:
[tex]f = \frac{1}{\frac{x+\epsilon-5}{x+\epsilon} }[/tex]
[tex]f = \frac{1}{1-\frac{5}{x+\epsilon} }[/tex]
Let be [tex]x = 5[/tex], as [tex]\epsilon[/tex] is approaching zero, [tex]f[/tex] is positive and becomes bigger, diverging to [tex]+\infty[/tex].
The right-hand limit of as x approaches f(x) = x/x-5 as x approaches 5 is +∞.
An integral in mathematics is either a numerical value equal to the area under the graph of a function for some interval or a new function, the derivative of which is the original function (indefinite integral).
Given function : f(x)= x/(x-5)
The expression for right- hand limit is
f(x)= x+c/(x+c-5)
So,
f(x)= 1/ (x+c-5)/ x+c
Using, the partial fraction we get
(x+c-5)/ x+c= 1- 5/(x+c)
So,
f(x)= 1/1- 5/(x+c)
let x=5 and c approaches to zero as it is arbitrary constant then f is positive and function will diverge to +∞.
Learn more about integrals here:
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