Question

Use the definition of continuity and the properties of limits to show that the function is continuous at the given number. f(x)=x^{2}+\sqrt{7-x}, a=4

Composite functions
ANSWERED
asked 2021-05-01
Use the definition of continuity and the properties of limits to show that the function is continuous at the given number.
\(\displaystyle{f{{\left({x}\right)}}}={x}^{{{2}}}+\sqrt{{{7}-{x}}},{a}={4}\)

Answers (1)

2021-05-02

\(\displaystyle\lim_{{{x}\rightarrow{4}}}{x}^{{{2}}}+\sqrt{{\lim_{{{x}\rightarrow{4}}}{7}-\lim_{{{x}\rightarrow{4}}}{x}}}\) Apply the Sum Law, Difference Law, and Root Law
\(\displaystyle{\left({4}\right)}^{{{2}}}+\sqrt{{{7}-{4}}}\) Plug in the corresponding values
\(\displaystyle{f{{\left({4}\right)}}}={16}+\sqrt{{{3}}}\) Evaluate
continuous f(4) is defined and equal to \(\displaystyle{16}+\sqrt{{{3}}}\) at \(x=4\), thus it is continuous at that point.

0
 
Best answer

expert advice

Need a better answer?
...