Mathematics, 17.06.2020 05:57 2020seogang
Let f ( x ) = e x − cos x , f(x)=ex−cosx, g ( x ) = e x + cos x , g(x)=ex+cosx, and h ( x ) = cos x . h(x)=cosx. Are f ( x ) , f(x), g ( x ) , g(x), and h ( x ) h(x) linearly independent? If so, show it, if not, find a linear combination that works.
Answers: 3
![det \left[\begin{array}{ccc}f(0)&g(0)&h(0)\\f(\frac{\pi}{2})&g(\frac{\pi}{2})&h(\frac{\pi}{2})\\f(\pi)&g(\pi)&h(\pi)\end{array}\right]](/tpl/images/0687/6318/53be6.png)
![det \left[\begin{array}{ccc}e^0-cos(0)&e^0+cos(0)&cos(0)\\e^{\frac{\pi}{2}}-cos(\frac{\pi}{2})&e^{\frac{\pi}{2}}+cos(\frac{\pi}{2})}&cos(\frac{\pi}{2})\\e^\pi-cos(\pi)&e^\pi+cos(0\pi)&cos(0\pi)\end{array}\right] =0](/tpl/images/0687/6318/f7add.png)
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Let f ( x ) = e x − cos x , f(x)=ex−cosx, g ( x ) = e x + cos x , g(x)=ex+cosx, and h ( x ) = cos...
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