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By use of calculus, show that x − ln(1 + x) is positive for all positive x.

Let f be a function defined on the positive real axis with values in R, such that f(x) = x - ln(1+x). Differentiating this function, we obtain, f'(x) = (x - ln(1+x))' = x' - ln'(1+x) = 1 - 1/(1+x). Sin...

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Answered by Andreea I. STEP tutor
13400 Views

How many distinct real roots does the equation x^3 − 30x^2 + 108x − 104 = 0 have?

We can see that 104 = 2^3 * 13 = 2226, 30 = 2 + 2 + 26, and 108 = 22 + 226 + 2*26, so the coefficients agree with the Vieta's formulas, so the roots of the equation above are 2, 2, 26...

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Answered by Andreea I. MAT tutor
9995 Views

Why do you want to be a doctor rather than a nurse?

This is a commonly asked question in medical interviews, however several people struggle to come up with a strong answer. 

MS
Answered by Molly S. UCAT tutor
3724 Views

How can I write a personal statement that doesn't sound arrogant?

This is something that everyone will struggle with: writing 4000 characters about how great you are will inevitably feel a bit awkward. The key is to be confident, but not cocky. You can do this in two wa...

MS
8280 Views

How do I prepare for the LNAT?

The best way to practise for the LNAT is to practise your reading and articulation skills. This can be done by reading a newspaper and thinking about the story you are reading: what is the main issue? wha...

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Answered by Olivia B. LNAT tutor
3440 Views

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