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.


Guest 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)

Melody  Oct 7, 2017

19 Online Users


New Privacy Policy

We use cookies to personalise content and advertisements and to analyse access to our website. Furthermore, our partners for online advertising receive information about your use of our website.
For more information: our cookie policy and privacy policy.