Chapter 2: Problem 39
In Exercises \(39-44,\) (a) find a power function end behavior model for \(f .\) (b) Identify any horizontal asymptotes. $$f(x)=3 x^{2}-2 x+1$$
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In Exercises 69-71, find the limit. Give a convincing argument that the value is correct. $$\lim _{x \rightarrow \infty} \frac{\ln x^{2}}{\ln x}$$
In Exercises \(31 - 36 ,\) determine the limit. $$\lim _ { x \rightarrow 0 ^ { + } } \frac { x } { | x | }$$
In Exercises \(59 - 62 ,\) find the limit graphically. Use the Sandwich Theorem to confirm your answer. $$\lim _ { x \rightarrow 0 } x ^ { 2 } \sin \frac { 1 } { x ^ { 2 } }$$
In Exercises \(55 - 58 ,\) complete parts \(( a ) - ( d )\) for the piecewise- definedfunction. \(\quad (\) a) Draw the graph of \(f\) . (b) At what points \(c\) in the domain of \(f\) does \(\lim _ { x \rightarrow c } f ( x )\) exist? (c) At what points \(c\) does only the left-hand limit exist? (d) At what points \(c\) does only the right-hand limit exist? $$f ( x ) = \left\\{ \begin{array} { l l } { \sqrt { 1 - x ^ { 2 } } , } & { 0 \leq x < 1 } \\ { 1 , } & { 1 \leq x < 2 } \\ { 2 , } & { x = 2 } \end{array} \right.$$
In Exercises \(15-18\) , determine whether the curve has a tangent at the indicated point, If it does, give its slope, If not, explain why not. $$f(x)=\left\\{\begin{array}{ll}{-x,} & {x<0} \\ {x^{2}-x,} & {x \geq 0}\end{array}\right.\( at \)x=0$$
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