Posted by Anonymous on Wednesday, October 7, 2009 at 10:50am.
The limit represents the derivative of some function f at some number a. Select an appropriate f(x) and a.
lim (cos(pi+h)+1)/h
h>0
answers are
f(x) = tan(x), a = pi
f(x) = cos(x), a = pi/4
f(x) = cos(x), a = pi
f(x) = sin(x), a = pi

calculus  bobpursley, Wednesday, October 7, 2009 at 11:31am
Using La'Hopital's rule...
lim = d/dx numerator/d/dx denominator
= sin(pi+h)(1)/1= sinPI
So none of the answers are really right, however, one can note that sinPI=sinPI=0, so the last answer is right because it is zero. However, one could have written just as well
f(x)= 40.3 sinPI and that would be right. And because of this, equalling zero, the first answer is just as right. The question is not well crafted, unless I missed something.
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