-4x is the slope and -12 is the y-intercept
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:

Step-by-step explanation:
We know that tangent angle addition formula is

This is in form already. Based on the value, a is 65 and b is 35 so let just subtract that

W e know that tan 30 is

Answer:
The area of the sector is 
Step-by-step explanation:
step 1
Find the area of complete circle

we have

substitute


step 2
Find the area of the sector
we know that
The area of complete circle subtends a central angle of 2π radians
so
using proportion
Find out the area of a sector by a central angle of 1/9 pi radians

15 pizzas
Explanation:
If there are 15 people, and each person eats 1 pizza, there must be 15 pizzas.