How do you evaluate the limit lim(x+sinx)dx as x->0?

1 Answer
Nov 16, 2017

lim_(xrarr0) (x+sin(x))dx=0

Explanation:

lim_(xrarr0) (x+sin(x))dx

color(white)("XXX")=color(blue)(lim_(xrarr0)x * dx) +color(magenta)(lim_(xrarr0)sin(x) * dx)

color(white)("XXX")=color(blue)( 0 * dx)+color(magenta)(0 * dx)

color(white)("XXX")=0

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Is it possible that the original question should have been:
color(white)("XXX")lim_(xrarr0) (d(x+sin(x)))/(dx)
or something else along those lines?