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Algebra
Pregunta

31-34 True-False Determine whether the statement i...

31-34 True-False Determine whether the statement is true or false. Explain your answer. 31. The equation of a tangent line to a differentiable function is a first-degree Taylor polynomial for that function. 32. The graph of a function \( f \) and the graph of its Maclaurin polynomial have a common \( y \) -intercept. 33. If \( p _ { 6 } ( x ) \) is the sixth-degree Taylor polynomial for a function 

\( f \) about \( x = x _ { 0 } \) , then \( p _ { 6 } ^ { ( 4 ) } ( x _ { 0 } ) = 4 ! f ^ { ( 4 ) } ( x _ { 0 } ) \) . 34. If \( p _ { 4 } ( x ) \) is the fourth-degree Maclaurin polynomial for \( e ^ { x } \) , then 

\( e ^ { 2 } - p _ { 4 } ( \overline { 2 } ) | \leq \frac { 9 } { 5 ! }\) 

Answer

34. False

\(|e^{2}- p_{4}(2)|= R_{4}(2)= \frac{e^{\varepsilon }}{5!}2^{5},\varepsilon \in(0,2) \\\Rightarrow |e^{2}- p_{4}(2)|> \frac{e^{0}}{5!}2^{5}= \frac{32}{5!}> \frac{9}{5!}\)

Solución
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