How do you find the limit of #(x+sinx)/x# as x approaches 0?
1 Answer
Mar 3, 2016
Explanation:
We will make use of the following trigonometric limit:
#lim_(xto0)sinx/x=1#
Let
Simplify the function:
#f(x)=x/x+sinx/x#
#f(x)=1+sinx/x#
Evaluate the limit:
#lim_(x to 0) (1+sinx/x)#
Split up the limit through addition:
#lim_(x to 0)1+lim_(x to 0)sinx/x#
#1+1=2#
We can check a graph of
graph{(x+sinx)/x [-5.55, 5.55, -1.664, 3.885]}
The graph does seem to include the point