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Sagot :
we have the function
[tex]f(x)=\frac{x+1}{x\sqrt[]{x}}[/tex]Complete the table
Substitute each value of x in the given function to obtain the value of f(x0
so
For x=10^0=1
[tex]f(x)=\frac{1+1}{1\sqrt[]{1}}=2[/tex]For x=10^1=10
[tex]f(x)=\frac{10+1}{10\sqrt[]{10}}=0.348[/tex]For x=10^2=100
[tex]f(x)=\frac{100+1}{100\sqrt[]{100}}=0.101[/tex]For x=10^3=1,000
[tex]f(x)=\frac{1000+1}{1000\sqrt[]{1000}}=0.032[/tex]For x=10^4=10,000
[tex]f(x)=\frac{10000+1}{10000\sqrt[]{10000}}=0.010[/tex]For x=10^5=100,000
[tex]f(x)=\frac{100000+1}{100000\sqrt[]{100000}}=0.003[/tex]For x=10^6=1,000,000
[tex]f(x)=\frac{1000000+1}{1000000\sqrt[]{1000000}}=0.001[/tex]therefore
[tex]\lim _{x\to\infty}f(x)=0[/tex]see the attached figure below
as the value of x increases -----> the value of f(x) decreases
as x ----> ∞ f(x) ---> 0
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