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Magazine Problem 4
In Exercises \(1-8\), evaluate the given limit. $$ \lim _{x \rightarrow 12}(3-x / 4) $$
Problem 4
Simplify the given expression. $$ \left(8^{\sqrt{3}} \cdot 4^{\sqrt{7}}\right) / 2^{\pi} $$
Problem 4
Determine whether the sequence \(\left\\{a_{n}\right\\}\) converges. If it does, state the limit. $$ a_{n}=3-(-1)^{n} $$
Problem 5
In Exercises \(1-8\), evaluate the given limit. $$ \lim _{x \rightarrow 0}(\sqrt{2}-\pi x) $$
Problem 5
Simplify the given expression. $$ \left(\sqrt{11}^{\sqrt{2}}\right)^{\sqrt{2}} $$
Problem 5
Determine the values at which the given function \(f\) is continuous. Remember that if \(c\) is not in the domain of \(f,\) then \(f\) cannot be continuous at \(c .\) Also remember that the domain of a function that is defined by an expression consists of all real numbers at which the expression can be evaluated. $$ f(x)=x^{2}+4 $$
Problem 5
Decide whether the indicated limit exists. If the limit does exist, compute it. $$ \lim _{h \rightarrow 1} \frac{h-3}{h+1} $$
Problem 5
In Exercises \(1-20\), determine whether the given limit exists. If it does exist, then compute it. $$ \lim _{x \rightarrow+\infty} \frac{x+\sqrt{x}}{x^{2}-\sqrt{x}} $$
Problem 5
Determine whether the sequence \(\left\\{a_{n}\right\\}\) converges. If it does, state the limit. $$ a_{n}=1 /(n+2) $$
Problem 6
Determine the values at which the given function \(f\) is continuous. Remember that if \(c\) is not in the domain of \(f,\) then \(f\) cannot be continuous at \(c .\) Also remember that the domain of a function that is defined by an expression consists of all real numbers at which the expression can be evaluated. $$ f(x)=2 x-9 $$
