limit of sin x / 2x squared - x as x approaches 0
You probably meant
Lim (sinx/(2x^2 - x) as x---> 0
then ....
= lim sinx/(x(2x-1)
= lim (sinx/x) (1/(2x-1) as x ---> 0
= (1)(1/(0-1)
= -1
To find the limit of sin(x) / (2x^2 - x) as x approaches 0, we can plug in x = 0 and check if the expression is defined or not. However, if you do this, you will get an indeterminate form of 0/0.
To evaluate this limit, we can simplify the expression and apply some algebraic techniques:
lim(x->0) sin(x) / (2x^2 - x)
We can factor out x from the denominator:
lim(x->0) sin(x) / x(2x - 1)
Now, we have sin(x) / x which is a well-known limit. The limit of sin(x)/x as x approaches 0 is equal to 1. So we can replace sin(x)/x with 1:
lim(x->0) 1 / (2x - 1)
Now, we can plug in x = 0 directly:
lim(x->0) 1 / (2*0 - 1) = 1 / (-1) = -1
Therefore, the limit of sin(x) / (2x^2 - x) as x approaches 0 is -1.