maths help (1 Viewer)

d3st1nyLiang

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1. how do you integrate this from -2 to 2?
http://integrals.wolfram.com/index.jsp?expr=xe^x^k&random=false

2. How do you show that the line y = x+1 is tangent to y = e^k

and prove with a diagram the e^x-x-1 = 0 has only 1 solution

3. Solve e^t - e^-t = 2
 

jet

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For the second question, you find the points where the gradient of y = e^x is 1 (i.e the gradient of y = x + 1). This should give you a single point. Drawing y = e^x on a graph and showing the tangent, it is obvious that the tangent only touches y = e^x once. Hence, there is one solution to e^x = x + 1 or, rewritten, e^x - x - 1 = 0
 

jet

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A question - are these 3 unit or 2 unit questions?
 

jet

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Well I don't see a method of doing that first question without 3u and 4u methods.
 

Trebla

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Is there a restriction on k? The definite integral equals zero if k is even.
 

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