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:
First answer is correct
Step-by-step explanation:
pi*r^2
use formula and substitute
r is the radius so half the diameter
Answer:
1. 80%
2. 125%
Step-by-step explanation:
1. 8 is 80% of 10.
2. 10 is 125% of 8.
Answer:
36
Step-by-step explanation:
Answer:
<h2>
</h2>
Explanation:
An equality can be transformed in a system of equations by making each side equal to a new variable. In this case the variable y was made equal to each side.
See that may find the solution of such system by graphing both functions in a same coordinate system, where the intersection of the functions would show the solution of the system.
I show you that in the attached image. In such graph, the red curve is the function y = x² and the blue function is y = x³ + 2x.
The intersection point is (0,0) meaning that the solution is x = 0, y = 0.
