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Effectus [21]
3 years ago
10

Prove: lim x^3 = 8. x approaches 2

Mathematics
1 answer:
Maslowich3 years ago
5 0
When we compute the value of a limit, all that we do is to change the value of the parameter
<span>lim x^3             = (2)^3= 2x2x2=8
</span><span>x approaches 2</span>
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Using the numbers 3, 2, and 4, which of these problems would have a solution of 4?
Alexeev081 [22]
Pemdas

ok if we look at the first one
exponents first
2^3=8
2^3=8
we have
4*8/8
4*8=32
32/8=4
das is answer


the first one is the answer
7 0
3 years ago
Remember to show work and explain. Use the math font.
MrMuchimi

Answer:

\large\boxed{1.\ f^{-1}(x)=4\log(x\sqrt[4]2)}\\\\\boxed{2.\ f^{-1}(x)=\log(x^5+5)}\\\\\boxed{3.\ f^{-1}(x)=\sqrt{4^{x-1}}}

Step-by-step explanation:

\log_ab=c\iff a^c=b\\\\n\log_ab=\log_ab^n\\\\a^{\log_ab}=b\\\\\log_aa^n=n\\\\\log_{10}a=\log a\\=============================

1.\\y=\left(\dfrac{5^x}{2}\right)^\frac{1}{4}\\\\\text{Exchange x and y. Solve for y:}\\\\\left(\dfrac{5^y}{2}\right)^\frac{1}{4}=x\qquad\text{use}\ \left(\dfrac{a}{b}\right)^n=\dfrac{a^n}{b^n}\\\\\dfrac{(5^y)^\frac{1}{4}}{2^\frac{1}{4}}=x\qquad\text{multiply both sides by }\ 2^\frac{1}{4}\\\\\left(5^y\right)^\frac{1}{4}=2^\frac{1}{4}x\qquad\text{use}\ (a^n)^m=a^{nm}\\\\5^{\frac{1}{4}y}=2^\frac{1}{4}x\qquad\log_5\ \text{of both sides}

\log_55^{\frac{1}{4}y}=\log_5\left(2^\frac{1}{4}x\right)\qquad\text{use}\ a^\frac{1}{n}=\sqrt[n]{a}\\\\\dfrac{1}{4}y=\log(x\sqrt[4]2)\qquad\text{multiply both sides by 4}\\\\y=4\log(x\sqrt[4]2)

--------------------------\\2.\\y=(10^x-5)^\frac{1}{5}\\\\\text{Exchange x and y. Solve for y:}\\\\(10^y-5)^\frac{1}{5}=x\qquad\text{5 power of both sides}\\\\\bigg[(10^y-5)^\frac{1}{5}\bigg]^5=x^5\qquad\text{use}\ (a^n)^m=a^{nm}\\\\(10^y-5)^{\frac{1}{5}\cdot5}=x^5\\\\10^y-5=x^5\qquad\text{add 5 to both sides}\\\\10^y=x^5+5\qquad\log\ \text{of both sides}\\\\\log10^y=\log(x^5+5)\Rightarrow y=\log(x^5+5)

--------------------------\\3.\\y=\log_4(4x^2)\\\\\text{Exchange x and y. Solve for y:}\\\\\log_4(4y^2)=x\Rightarrow4^{\log_4(4y^2)}=4^x\\\\4y^2=4^x\qquad\text{divide both sides by 4}\\\\y^2=\dfrac{4^x}{4}\qquad\text{use}\ \dfrac{a^n}{a^m}=a^{n-m}\\\\y^2=4^{x-1}\Rightarrow y=\sqrt{4^{x-1}}

6 0
3 years ago
66 dollars is fifteen % of what amount
inn [45]
66 is 15% of what amount....
66 = 0.15x
66/0.15 = x
440 = x......so $ 66 is 15% of $ 440
8 0
2 years ago
Not sure need help ​
lord [1]

Answer:

9

Step-by-step explanation:

3-2i+8=23

5+2i+23

2i=18

i=-9

3 0
2 years ago
I know it’s hard to read, but if u can, please help!!
Elden [556K]

Answer:

  4th choice (if we guessed the blurry letters properly)

Step-by-step explanation:

The reflection maps ...

  (x, y) ⇒ (x -y)

Then the rotation maps ...

  (x, -y) ⇒ (y, x)

That is, R(-1, 4) becomes R'(4, -1), apparently matching point S, the only point at (4, -1). We can't read the letters, but we know that you only need to know where R ends up in order to select the correct answer.

3 0
3 years ago
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