Simple Core 3 verification wanted - large values of lns -> converge or diverge where? Watch

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Report Thread starter 12 years ago
Hello, the question I have is "Given f(x) = ln x, sketch on the same diagram the graphs of y = f(x) and y = 4f(x-1). Label the coordinates of the point of intersection of each of the graphs with the x axis. Indicate the behaviour of each of the graphs for large positive and large negative values of y."

Large negative values of the f(x) would converge towards 0, and large negative values of 4f(x-1) would converge towards 1. What would happen to large positive values, though?
div curl F = 0
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Report 12 years ago

For large positive values of Y (Y = Ln(x) ----> x = exp(Y) and Y = 4Ln(x-1) ----> x = 1 + exp(Y/4)), X tends to infinity, i.e. the function blows up, however the gradient becomes smaller and smaller until it reaches infinity where the gradient becomes zero. So the function will tend to infinity as X tends to infinity and the gradient will tend to zero as X -----> V.Large.

Hope this helps

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