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A distortion in spacetime! This is worrying to say the least. What could this alien race be planning? You decide you need to learn more about this distortion. For starters, you need to get some estimate of the size of the distortion. To do this, you use the available images to construct a power series centred at a point x = 10 (in units of km) along a linear axis in space. The radius of convergence of this power series should equal the radius of the spacetime distortion. Sampling some x values, you find that the power series: • is convergent when x = -60, –30, and 30, and • is divergent when x = -100, –90, and 140. Based on this information, what are the minimum and maximum possible values for the radius of the spacetime distortion (in units of km)? Rmin Rmax

A distortion in spacetime! This is worrying to say the least. What could this alien race be planning? You decide you need to learn more about this distortion. For starters, you need to get some estimate of the size of the distortion. To do this, you use the available images to construct a power series centred at a point x = 10 (in units of km) along a linear axis in space. The radius of convergence of this power series should equal the radius of the spacetime distortion. Sampling some x values, you find that the power series: • is convergent when x = -60, –30, and 30, and • is divergent when x = -100, –90, and 140. Based on this information, what are the minimum and maximum possible values for the radius of the spacetime distortion (in units of km)? Rmin Rmax

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A distortion in spacetime! This is worrying to say the least. What could this alien race be planning? You decide you need to learn more about this distortion. For starters, you need to get some estimate of the size of the distortion. To do this, you use the available images to construct a power series centred at a point x = 10 (in units of km) along a linear axis in space. The radius of convergence of this power series should equal the radius of the spacetime distortion. Sampling some x values, you find that the power series: • is convergent when x = -60, –30, and 30, and • is divergent when x = –100, –90, and 140. Based on this information, what are the minimum and maximum possible values for the radius of the spacetime distortion (in units of km)? Rmin Rmaz ||
Transcribed Image Text:A distortion in spacetime! This is worrying to say the least. What could this alien race be planning? You decide you need to learn more about this distortion. For starters, you need to get some estimate of the size of the distortion. To do this, you use the available images to construct a power series centred at a point x = 10 (in units of km) along a linear axis in space. The radius of convergence of this power series should equal the radius of the spacetime distortion. Sampling some x values, you find that the power series: • is convergent when x = -60, –30, and 30, and • is divergent when x = –100, –90, and 140. Based on this information, what are the minimum and maximum possible values for the radius of the spacetime distortion (in units of km)? Rmin Rmaz ||
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