Limx→+∞ (x-(lnx)^2) =?

1 answer:

3 0

$\lim_{x\to\infty}(x-\ln(x)^2) \\\lim_{x\to\infty}(x-2\ln(x)) \\\lim_{x\to\infty}\Big(x\Big(1-\dfrac{2\ln(x)}{x}\Big)\Big) \\\lim_{x\to\infty}x\cdot\lim_{x\to\infty}\Big(1-\dfrac{2\ln(x)}{x}\Big) \\\infty\cdot\Big(\lim_{x\to\infty}(1)-\lim_{x\to\infty}\Big(\dfrac{2\ln(x)}{x}\Big)\Big) \\\infty\cdot(1-2\lim_{x\to\infty}(1/x)) \\\infty\cdot(1-0) \\\infty\cdot1=\boxed{\infty}$

Hope this helps.

You might be interested in

Select "Growth" or "Decay" to classify each function.

allochka39001 [22]

1. The growth rate equation has a general form of:

y = A (r)^t

The function is growth when r≥1, and it is a decay when r<1. Therefore:

y=200(0.5)^2t --> Decay

y=1/2(2.5)^t/6 --> Growth

y=(0.65)^t/4 --> Decay

2. We rewrite the given equation (1/3)^d−5 = 81

Take the log of both sides:

(d – 5) log(1/3) = log 81

d – 5 = log 81 / log(1/3)

d – 5 = - 4

Multiply both sides by negative 1:

- d + 5 = 4

So the answer is D

5 0

3 years ago

Ace scored 3 baskets in his second game of the season. This was 2 less than his first game. What was the percent change between

Alex_Xolod [135]

Answer:

2% different

Step-by-step explanation:

it is 2% different because if Ace scored 3 baskets in his scond game but it was 2 less then his first so which means his first game he scored 5

6 0

3 years ago

What is thr inverse of f(x) if the function is x=-4,-2,0,2,4 f(x)=-2,-1,0,1,2

Lorico [155]

For a function, if it has an inverse function, keep in mind that, the "domain of the original, is the range of the inverse, and the range of the original, is the domain of the inverse", what the dickens does that mean?

well, it means the values for "x" and f(x), on the inverse, are the same values, but swapped up, therefore

$\bf \stackrel{original~function}{\begin{array}{ccll}
x&f(x)\\
\text{\textemdash\textemdash\textemdash}&\text{\textemdash\textemdash\textemdash}\\
-4&-2\\
-2&-1\\
0&0\\
2&1\\
4&2
\end{array}}\qquad \qquad \qquad 
\stackrel{inverse~function}{\begin{array}{ccll}
x&f(x)\\
\text{\textemdash\textemdash\textemdash}&\text{\textemdash\textemdash\textemdash}\\
-2&-4\\
-1&-2\\
0&0\\
1&2\\
2&4
\end{array}}$

7 0

3 years ago

Write a number in each blank to complete each equation so that it has the requested number of solutions. a. Equation with no sol

Setler79 [48]

Answer:

The answer is 8 $x$ - 3 $x$ + 2 - $x$ = 4  $x$ + 2  .