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Let F(x)and G(x)be Two Functions H(0)H ^ { \prime } ( 0 )

question 63

Multiple Choice

Let f(x) and g(x) be two functions.Values of f(x) , f '(x) , g(x) , and g'(x) for x = 0, 1, and 2 are given in the table below.Use the information in the table to find H(0) H ^ { \prime } ( 0 ) if H(x) =H ( x ) = e g(x)
+π+ \pi x.
xf(x) f(x) g(x) g(x) 0112511240273110.5\begin{array} { c c c c c } \boldsymbol { x } & f ( x ) & f ^ { \prime } ( x ) & g ( x ) & g ^ { \prime } ( x ) \\0 & 1 & - 1 & 2 & 5 \\1 & - 1 & 2 & 4 & 0 \\2 & 7 & 3 & 11 & 0.5\end{array}

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