MHB 2.3.361 AP Calculus Exam of differentials of sin wave

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The discussion revolves around duplicating a sine wave graph using Desmos, with participants questioning the nature of the function involved. There's a debate on whether the function is a trigonometric function or potentially a polynomial of degree 3. The conversation highlights that understanding the derivatives of sine and cosine can aid in recognizing transformations in the graph. Additionally, it emphasizes that the equation of the curve is not necessary to make accurate choices regarding the function's behavior. The thread underscores the importance of analyzing derivatives and integrals in calculus to understand function characteristics.
karush
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image due to graph, I tried to duplicate this sin wave on desmos but was not able to.

so with sin and cos it just switches to back and forth for the derivatives so thot a this could be done just by observation but doesn't the graph move by the transformations

well anyway?
 

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what makes you think it's a trig function ? ... could it also be a polynomial function of degree 3 ? note my calc screenshotas you stated, you don't need the equation of the curve to make the correct choice ...

$\displaystyle h(6) = \int_0^6 f(t) \, dt < 0$

$h'(6) = f(6) = 0$

$h''(6) = f'(6) > 0$
 

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Thread 'Problem with calculating projections of curl using rotation of contour'

Thread 'Problem with calculating projections of curl using rotation of contour'

Hello! I tried to calculate projections of curl using rotation of coordinate system but I encountered with following problem. Given: ##rot_xA=\frac{\partial A_z}{\partial y}-\frac{\partial A_y}{\partial z}=0## ##rot_yA=\frac{\partial A_x}{\partial z}-\frac{\partial A_z}{\partial x}=1## ##rot_zA=\frac{\partial A_y}{\partial x}-\frac{\partial A_x}{\partial y}=0## I rotated ##yz##-plane of this coordinate system by an angle ##45## degrees about ##x##-axis and used rotation matrix to...
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