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Artyom0805 [142]
4 years ago
14

3.

Mathematics
1 answer:
krek1111 [17]4 years ago
6 0

Answer:

2

Step-by-step explanation:

Let L be a real number.

\lim_{x \rightarrow 2}f(x) equals L if:

\lim_{x \rightarrow 2^-}f(x)=L

\lim_{x \rightarrow 2^+}f(x)=L

----------------------------

\lim_{x \rightarrow 2^-}f(x) means what does y get close to as we move x closer to 2 from the left. Please look at the orange to see what that looks like visually.

We see that y tends to 2.

This means:

\lim_{x \rightarrow 2^-}f(x)=2

-----------------------------

\lim_{x \rightarrow 2^+}f(x) means what does y get close to as we move x closer to 2 from the right. Please look at the blue to see what that looks like visually.

We see that y tends to 2.

This means:

\lim_{x \rightarrow 2^+}f(x)=2

----------------------------

Therefore,

\lim_{x \rightarrow 2}f(x)=2.

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Alecsey [184]

Answer:

Quantity of soap left after Juan washes 8 regular loads and 5 heavy loads of laundry =12.9 pounds.

Step-by-step explanation:

Number of scoop of soap used to wash a regular load of laundry = One 0.15 pound scoop

Number of scoops of soap used to wash heavy work clothes = Two 0.15 pound scoops

As Juan washes 8 regular loads and 5 heavy loads of laundry,

Total quantity of soap used = 8(0.15)+5(2)(0.15)=1.2+1.5=2.7 pounds

As a box of laundry soap weighed 15.6 pounds,

quantity of soap left after Juan washes 8 regular loads and 5 heavy loads of laundry =15.6-2.7=12.9 pounds.

8 0
3 years ago
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Step-by-step explanation:

8 0
2 years ago
Determine the commutators of the operators a and a+,where a = (x + ip)/2 ^1/2 and a+ = (x - ip)/ 2 ^1/2
Vsevolod [243]

Answer:

Given that:

a = (\frac{x+ip}{2})^{\frac{1}{2}} and a+= (\frac{x-ip}{2})^{\frac{1}{2}}

if a , a+ commutator, it obeys aa^+ = a^+a

First find:

aa^+ = (\frac{x+ip}{2})^{\frac{1}{2}} (\frac{x-ip}{2})^{\frac{1}{2}}

                = (\frac{(x)^2-(ip)^2}{4})^{\frac{1}{2}}=(\frac{(x)^2+(p)^2}{4})^{\frac{1}{2}}

Now;

a^+a =(\frac{x-ip}{2})^{\frac{1}{2}} (\frac{x+ip}{2})^{\frac{1}{2}} = (\frac{(x)^2-(ip)^2}{4})^{\frac{1}{2}}

              =(\frac{(x)^2-(ip)^2}{4})^{\frac{1}{2}}=(\frac{(x)^2+(p)^2}{4})^{\frac{1}{2}}

therefore, aa^+ = a^+a which implies the operators a and a+ are commutators.    


7 0
3 years ago
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iragen [17]

Each term has a common divisor of 12^{11}:

12^{13}-12^{12}+12^{11}=12^{11}(12^2-12+1)=12^{11}\cdot133

133 = 7*19, so the number in the blanks is 12^{11}.

3 0
3 years ago
What expressions are equivalent to -56z + 28
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Answer:

3b+b and 2(2b)

Step-by-step explanation:


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