Combine the two fractions in the numerator, and then simplify. This problem isn't much more than an exercise in working with fractions.Alice7979 said:Homework Statement
lim (1/x - 1/3) / (x-3)
x->3
Homework Equations
The Attempt at a Solution
I tried to cancel the bottom (x-3) out by multiplying the top by 3/3 and x/x and then got ((3-x)/3x)/(x-3) but ended with 0/0 and the right answer is -1/9. The top part is confusing me.
The quotient law for limits states that the limit of a quotient is equal to the quotient of the limits of the individual functions, as long as the limit of the denominator is not equal to zero.
To apply the quotient law, you first find the limits of the numerator and denominator separately. Then, you can take the quotient of these limits to find the overall limit.
If the limit of the denominator is zero, the quotient law cannot be applied. This is because dividing by zero is undefined in mathematics.
Yes, the quotient law can be used for all types of functions, as long as the limit of the denominator is not equal to zero.
Yes, there are other laws for finding limits, such as the sum and difference laws, product law, and power law. These laws can be used in combination with the quotient law to find limits of more complex functions.