Find the limit. Use l'Hospital's Rule where appropriate. If there is a more elementary method, consider using it.
lim
x → 0
(x 6x)/(6x − 1)
To find the limit of the expression using l'Hospital's Rule, we first differentiate the numerator and the denominator separately.
The derivative of x^6 is 6x^5, and the derivative of 6x - 1 is 6.
So, using l'Hospital's Rule, the limit becomes:
lim (x^6 * 6x^5)/(6) as x approaches 0.
Simplifying the expression, we get:
lim (x^6 * x^5)/1 as x approaches 0.
Further simplifying, we have:
lim x^11 as x approaches 0.
Since this is a power function, we can directly evaluate this limit. When x approaches 0, x^11 will also approach 0.
Therefore, the limit is 0.
Not sure what (x 6x) means.
x+6x
x*6x
x^(6x)
??
In any case, using l'Hospital's Rule, the derivative of 6x-1 = 6, which does not vanish.