91Ó°ÊÓ

Solving Equations Is any real number exactly 1 less than its fourth power? Give any such values accurate to 3 decimal places.

In Exercises 45-48, find (a) a simple basic function as a right end behavior model and (b) a simple basic function as a left end behavior model for the function. $$y=e^{x}-2 x$$

Solving Equations Is any real number exactly 2 more than its cube? Give any such values accurate to 3 decimal places.

Continuous Function Find a value for \(a\) so that the function $$f(x)=\left\\{\begin{array}{ll}{x^{2}-1,} & {x<3} \\ {2 a x,} & {x \geq 3}\end{array}\right.$$ is continuous.

In Exercises 47 and 48 , determine whether the graph of the function has a tangent at the origin. Explain your answer. $$f(x)=\left\\{\begin{array}{ll}{x^{2} \sin \frac{1}{x},} & {x \neq 0} \\\ {0,} & {x=0}\end{array}\right.$$

In Exercises 47 and 48 , determine whether the graph of the function has a tangent at the origin. Explain your answer. $$f(x)=\left\\{\begin{array}{ll}{x \sin \frac{1}{x},} & {x \neq 0} \\ {0,} & {x=0}\end{array}\right.$$

In Exercises 45-48, find (a) a simple basic function as a right end behavior model and (b) a simple basic function as a left end behavior model for the function. $$y=x^{2}+\sin x$$

Continuous Function Find a value for \(a\) so that the function \(f(x)=\left\\{\begin{array}{ll}{2 x+3,} & {x \leq 2} \\ {a x+1,} & {x>2}\end{array}\right.\) is continuous.

Sine Function Estimate the slope of the curve \(y=\sin x\) at \(x=1 .\) (Hint: See Exercises 41 and $42 . )

Continuous Function Find a value for \(a\) so that the function $$f(x)=\left\\{\begin{array}{ll}{4-x^{2},} & {x<-1} \\ {a x^{2}-1,} & {x \geq-1}\end{array}\right.$$ is continuous.