Xm=x+z ,solve for x, Algebra 1
1 answer:
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Answer:
-1
Step-by-step explanation:
The expression evaluates to the indeterminate form -∞/∞, so L'Hopital's rule is appropriately applied. We assume this is the common log.
d(log(x))/dx = 1/(x·ln(10))
d(log(cot(x)))/dx = 1/(cot(x)·ln(10)·(-csc²(x)) = -1/(sin(x)·cos(x)·ln(10))
Then the ratio of these derivatives is ...
lim = -sin(x)cos(x)·ln(10)/(x·ln(10)) = -sin(x)cos(x)/x
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At x=0, this has the indeterminate form 0/0, so L'Hopital's rule can be applied again.
d(-sin(x)cos(x))/dx = -cos(2x)
dx/dx = 1
so the limit is ...
lim = -cos(2x)/1
lim = -1 when evaluated at x=0.
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I find it useful to use a graphing calculator to give an estimate of the limit of an indeterminate form.
Answer: The answer is a polynomial in two variables with degree 3.
Step-by-step explanation: We are given to write the properties of the polynomial
We can see that the polynomial 'p' contains two unknown variables 'x' and 'y'.
Also, the degree of the polynomial is the degree of the expression
Therefore, the degree of the polynomial will be 2 + 1 = 3.
Thus,
(i) the polynomial has two unknown variables 'x' and 'y', and
(ii) Its degree is 3.