Question

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

Answer 1

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.