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:
21 and 26 totaling 47sticks
Step-by-step explanation:
Th number of sticks form an arithmetic progression
1, 6, 11, 16...
The nth term of an arithmetic progression is expressed as;
Tn = a+(n-1)d
a is the first term = 1
d is the common difference
d = 6-1 = 11-6 = 5
n is the number of terms
The next two terms are the fifth and sixth term
T5 = 1+(5-1)5
T5 = 1+4(5)
T5 = 1+20
T5 = 21
T6 = 1+(6-1)5
T6 = 1+5(5)
T6 = 1+25
T6 = 26
Hence the number of sticks needed in the next two piles are 21 and 26 totaling 47sticks
Answer:
The surface area of square pyramid is 953.64 cm² .
Step-by-step explanation:
Given as for a square pyramid :
The height of pyramid = l = 15 cm
The base of square pyramid = x = 18 cm
Now,
The surface area of square Pyramid = 
or , The surface area of square Pyramid = 
Or, The surface area of square Pyramid = 
Or, The surface area of square Pyramid = 324 + 36 × 
or, The surface area of square Pyramid = 324 + 36 × 17.49
Or , The surface area of square Pyramid = 324 + 629.64 = 953.64 cm²
Hence The surface area of square pyramid is 953.64 cm² . Answer
Answer:
1, 2, or 3
Step-by-step explanation:
if it's third degree then there must me 1 to 3 roots
hope you find this helpful :)