91Ó°ÊÓ

Give the intervals on which the given function is continuous. $$ f(x)=\sin \left(e^{x}+x^{2}\right) $$

Use the Squeeze Theorem, where appropriate, to evaluate the given limit. $$ \lim _{x \rightarrow 0} x \sin \left(\frac{1}{x}\right) $$

Test your understanding of the Intermediate Value Theorem. Let \(f\) be continuous on [1,5] where \(f(1)=-2\) and \(f(5)=\) -10. Does a value \(1

Test your understanding of the Intermediate Value Theorem. Let \(g\) be continuous on [-3,7] where \(g(0)=0\) and \(g(2)=\) 25. Does a value \(-3

Use the Squeeze Theorem, where appropriate, to evaluate the given limit. $$ \lim _{x \rightarrow 0} \sin x \cos \left(\frac{1}{x^{2}}\right) $$

Test your understanding of the Intermediate Value Theorem. Let \(f\) be continuous on [-1,1] where \(f(-1)=-10\) and \(f(1)=10\). Does a value \(-1

Use the Squeeze Theorem, where appropriate, to evaluate the given limit. $$ \lim _{x \rightarrow 1} f(x), \text { where } 3 x-2 \leq f(x) \leq x^{3} $$

Use the Squeeze Theorem, where appropriate, to evaluate the given limit. $$ \lim _{x \rightarrow 3} f(x), \text { where } 6 x-9 \leq f(x) \leq x^{2} $$

Challenge your understanding of limits but can be evaluated using the knowledge gained in this section. $$ \lim _{x \rightarrow 0} \frac{\sin 3 x}{x} $$

Use the Bisection Method to approximate, accurate to two decimal places, the value of the root of the given function in the given interval. $$ f(x)=x^{2}+2 x-4 \text { on }[1,1.5] $$