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11. [-/7.5 Points] DETAILS Consider the following functions. $f_1(x) = e^x$, $f_2(x) = e^{-x}$, $f_3(x) = \sinh(x)$ $g(x) = c_1f_1(x) + c_2f_2(x) + c_3f_3(x)$ Solve for $c_1$, $c_2$, and $c_3$ so that $g(x) = 0$ on the interval $(-\infty, \infty)$. If a nontrivial solution exists, state it. (If only the trivial solution exists, enter the trivial solution $(0, 0, 0)$.) $\{c_1, c_2, c_3\} = \{ \}$ Determine whether $f_1, f_2, f_3$ are linearly independent on the interval $(-\infty, \infty)$. $\circ$ linearly dependent $\circ$ linearly independent

          11. [-/7.5 Points]
DETAILS
Consider the following functions.
$f_1(x) = e^x$, $f_2(x) = e^{-x}$, $f_3(x) = \sinh(x)$
$g(x) = c_1f_1(x) + c_2f_2(x) + c_3f_3(x)$
Solve for $c_1$, $c_2$, and $c_3$ so that $g(x) = 0$ on the interval $(-\infty, \infty)$. If a nontrivial solution exists, state it. (If only the trivial solution exists, enter the trivial solution $(0, 0, 0)$.)
$\{c_1, c_2, c_3\} = \{
\}$ 
Determine whether $f_1, f_2, f_3$ are linearly independent on the interval $(-\infty, \infty)$.
$\circ$ linearly dependent
$\circ$ linearly independent

$11. [-/7.5 Points] DETAILS Consider the following functions. f1(x) = e^x, f2(x) = e^-x, f3(x) = sinh(x) g(x) = c1f1(x) + c2f2(x) + c3f3(x) Solve for c1, c2, and c3 so that g(x) = 0 on the interval (-∞, ∞). If a nontrivial solution exists, state it. (If only the trivial solution exists, enter the trivial solution (0, 0, 0).) {c1, c2, c3} = {} Determine whether f1, f2, f3 are linearly independent on the interval (-∞, ∞). ∘ linearly dependent ∘ linearly independent$

Added by Miguel M.

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