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I got some values, but i would like to get a break down how to approach a problem like this. I have a book but it doesnt explain steps the way that helps me. I plugged in the X values into the function and got values from 0.9-1.01. But i dont know what to do after.


 Oct 6, 2017


P(0,1)       Q(x)=e^x


Let the  gradient of the secant PQ = m


 \(m=\frac{Q(x)-1}{x-0}=\frac{Q(x)-1}{x}\\ When \;\;x=-0.1\qquad\;\; m=\frac{e^{-0.1}-1}{-0.1}=0.952\\ When \;\;x=-0.01\qquad m=\frac{e^{-0.01}-1}{-0.01}=0.995\\ When \;\;x=-0.001\qquad m=\frac{e^{-0.001}-1}{-0.001}=1.000\\ When \;\;x=0.001\qquad m=\frac{e^{0.001}-1}{0.001}=1.001\\ When \;\;x=0.01\qquad m=\frac{e^{0.01}-1}{0.01}=1.005\\ When \;\;x=0.1\qquad m=\frac{e^{0.1}-1}{0.1}=1.052\\\)


Just looking at thes numbers it seems reasonable that the gradient of the tangent to y=e^x where x=0 is about 1

(And in fact it really is 1)

 Oct 7, 2017

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