What is the value if we substitute infinite to (-1/c)*x*e^(-cx)? Help me please..

1 Answer
Mar 17, 2018

#lim_(x->\infty) -1/c x e^(-cx)=0#

Explanation:

Assuming #c# is a positive constant...

#f(x) = -1/c x e^(-cx)#

#f(x) = -1/cx/(e^(cx))#

The limit is:

#lim_(x->\infty) f(x) = lim_(x->\infty) -1/c x/(e^(cx))#

# = -1/c lim_(x->\infty)x/(e^(cx))#

Use L'Hospital's rule:

#= -1/c lim_(x->\infty) 1/(c(e^(cx))#

#= -1/c^2 lim_(x->\infty) e^(-cx)#

#= -1/c^2(0) = 0#