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professor190 [17]
3 years ago
6

Limit as x approaches 0 of csc3x/cotx

Mathematics
1 answer:
jolli1 [7]3 years ago
6 0
Hello Meggieh821, to find the lim as x approaches 0 we can check this by inserting a number that is close to 0 that is coming from the left and from the right.

For instance, we can find the lim by using the number -.00001 for x and solve
<span>csc(3x) / cot(x)
</span>csc(3*-.00001) / cot(-.00001) = .333333... = 1 /3

We also need to check coming from the right. We will use the number .00001 for x
csc(3x) / cot(x)
csc(3*.00001) / cot(.00001) = .333333... = 1 /3

So since we are getting 1/3 from the left and right we can say as x approaches 0 the limit is 1/3

<span>\lim_{x\to 0} \frac{csc(3x)}{cot(x)} = \frac{1}{3}</span>

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Not sure how to do #69, it's a calc 1 question
Gnoma [55]
Let A( t , f( t ) ) be the point(s) at which the graph of the function has a horizontal tangent => f ' ( t ) = 0.

But, f ' ( x ) = [ ( x^2 ) ' * ( x - 1 ) - ( x^2 ) * ( x - 1 )' ] / ( x - 1 )^2 =>
f ' ( x ) = [ 2x( x - 1 ) - ( x^2 ) * 1 ] / ( x - 1 )^2 => f ' ( x ) = ( x^2 - 2x ) / ( x - 1 )^2;

f ' ( t ) = 0 <=> t^2 - 2t = 0 <=> t * ( t - 2 ) = 0 <=> t = 0 or t = 2 => f ( 0 ) = 0; f ( 2 ) = 4 => A 1 ( 0 , 0 ) and A 2 ( 2 , 4 ).
3 0
3 years ago
What is n in 3/5n + 15 =10+2/5n
Phantasy [73]
Simplify both sides of the equation.

<span><span><span><span>3/5</span>n </span>+ 15 </span>= <span><span><span>2/5</span>n </span>+ 10


</span></span>Subtract 2/5n from both sides.

<span><span><span><span><span>3/5</span>n </span>+ 15 - </span><span><span>2/5</span>n </span></span>= <span><span><span><span>2/5</span>n </span>+ 10 - </span><span><span>2/5</span>n</span></span></span><span><span><span><span>15</span>n </span>+ 15 </span>= 10


</span>Subtract 15 from both sides.

<span><span><span><span><span>1/5</span>n </span>+ 15 - </span>15 </span>= <span>10 - 15</span></span><span><span><span>1/5</span>n </span>= -<span>5


</span></span>Multiply both sides by 5.

<span><span>5 </span></span>× (1/5n) = (5) × (−5)<span>n = -<span><span>25


Answer: n is -25.</span></span></span>
8 0
3 years ago
Read 2 more answers
Rob needs to mix 4.5 liters of liquid fruit punch concentrate with 0.5
Dmitriy789 [7]
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7 0
2 years ago
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Tatiana [17]
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7 0
3 years ago
Solve the equation 7/z-1 = 9/z+4
algol [13]

Answer:

z is equal to 18.5

Step-by-step explanation:

When an equation is in the format a/b = c/d, the quickest way to simplify it is to cross multiply.  Each side is multiplied by the other sides denominator, eliminating the division:

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So z is equal to 18.5

3 0
3 years ago
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