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Elina [12.6K]
3 years ago
15

What is the range of the function represented by these ordered pairs?

Mathematics
2 answers:
loris [4]3 years ago
6 0
Hope this helps but the answer is A.
irinina [24]3 years ago
5 0
I believe it is b and hmu?
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Hiiii.. please help me with this limit question ​
Alenkasestr [34]

Answer:

π

Step-by-step explanation:

Solving without L'Hopital's rule:

lim(x→0) sin(π cos²x) / x²

Use Pythagorean identity:

lim(x→0) sin(π (1 − sin²x)) / x²

lim(x→0) sin(π − π sin²x) / x²

Use angle difference formula:

lim(x→0) [ sin(π) cos(-π sin²x) − cos(π) sin(-π sin²x) ] / x²

lim(x→0) -sin(-π sin²x) / x²

Use angle reflection formula:

lim(x→0) sin(π sin²x) / x²

Now we multiply by π sin²x / π sin²x.

lim(x→0) [ sin(π sin²x) / x² ] (π sin²x / π sin²x)

lim(x→0) [ sin(π sin²x) / π sin²x] (π sin²x / x²)

lim(x→0) [ sin(π sin²x) / π sin²x] lim(x→0) (π sin²x / x²)

π lim(x→0) [ sin(π sin²x) / π sin²x] [lim(x→0) (sin x / x)]²

Use identity lim(u→0) (sin u / u) = 1.

π (1) (1)²

π

Solving with L'Hopital's rule:

If we plug in x = 0, the limit evaluates to 0/0.  So using L'Hopital's rule:

lim(x→0) [ cos(π cos²x) (-2π cos x sin x) ] / 2x

lim(x→0) [ -π cos(π cos²x) sin(2x) ] / 2x

-π/2 lim(x→0) [ cos(π cos²x) sin(2x) ] / x

Again, the limit evaluates to 0/0.  So using L'Hopital's rule one more time:

-π/2 lim(x→0) [ cos(π cos²x) (2 cos(2x)) + (-sin(π cos²x) (-2π cos x sin x)) sin(2x) ] / 1

-π/2 lim(x→0) [ 2 cos(π cos²x) cos(2x) + π sin(π cos²x) sin²(2x) ]

-π/2 (-2)

π

8 0
2 years ago
the snack shack is making a batch of trail mix. they use 9 1/3 pounds of granola, 9 1/3 pounds of mixed nuts, and 9 1/3 pounds o
iris [78.8K]
9 1/3•3 = 28

28/14 = 2
2 pounds in each bag
4 0
2 years ago
You've been given a pay rise on your paper round you used to get paid £5 per hour but this has been increased by 20% how much wi
Allushta [10]

Answer:

20+5=25

Step-by-step explanation:

8 0
2 years ago
Factoring Trinomials
alexandr402 [8]
25 a² + 20 ab +  4 b²

for formula a^x+bx^ky^k+cy ^{2k } find  u,v such that: u.v = a

and u+v = b  then  group according to (ax ^{2k} +ux^ky^k)+(vx^ky^k+cy ^{2k} )

= (25a^2+10ab)+(10ab+4b^2)

factor out 5a from : 25a^2+10ab : 5a(2b+5a)

factor out 2b from : 10ab+4b^2: 2b(2b+5a)

= 5a(2b+5a) + 2b(2b+5a)

factor out : (5a+2b)

= (5a+2b)(5a+2b)

Refine:

(2b+5a)^2

hope this helps!.


3 0
3 years ago
Help with number27 and show work!
Dahasolnce [82]
1080 cm^2 you multiply 90*12 and that gives you your answer
6 0
3 years ago
Read 2 more answers
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