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3 years ago

Limit xtens to 0 x^2logx^2 what is the ans of interminate forms?

Mathematics

1 answer:

GarryVolchara [31]3 years ago

7 0

Rewrite the limit as

$\displaystyle\lim_{x\to0}x^2\log x^2=\lim_{x\to0}\frac{\log x^2}{\frac1{x^2}}$

Then both numerator and denominator approach infinity (with different signs, but that's not important). Applying L'Hopital's rule, we get

$\displaystyle\lim_{x\to0}\frac{\log x^2}{\frac1{x^2}}=\lim_{x\to0}\frac{\frac2x}{-\frac2{x^3}}=\lim_{x\to0}-x^2=\boxed{0}$

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Find the maximum value or minimum value for the function f(x) = 0.15(x + 1)² - 3.

il63 [147K]

Answer:

The minimum value for $f(x) = 0.15(x + 1)^2 - 3$ is $-3$ .

Step-by-step explanation:

Given function is $f(x) = 0.15(x + 1)^2 - 3$

We need to find the maximum value or the minimum value for the function.

Now, differentiate $f(x) = 0.15(x + 1)^2 - 3$ w.r.t $x$ .

$f'(x) =\frac{d}{dx}(0.15(x + 1)^2 - 3)\\f'(x)=\frac{d}{dx}(0.15(x+1)^2-\frac{d}{dx}(3)\\$

$f'(x)=2\times 0.15(x+1)\frac{d}{dx}(x+1)-0\\f'(x)=0.3(x+1)(1)\\f'(x)=0.3(x+1)$

Now, we will equate $f'(x)=0$ to find critical point.

$0.3(x+1)=0\\x=-1$

Plug this critical point in to the function $f(x) = 0.15(x + 1)^2 - 3$ we get,

$f(-1) = 0.15(-1 + 1)^2 - 3\\f(-1)=-3$

Also, $f''(x)=0.3$ which is positive, We have minimum value.

So, the minimum value for $f(x) = 0.15(x + 1)^2 - 3$ is $-3$ .

7 0

4 years ago

Graph the linear inequality: 2x + 3y = 12, by creating a t-chart to plot the points. Shade by

Crazy boy [7]

Answer:

See explanation

Step-by-step explanation:

Assuming the given inequality is $2x+3y\le12$

Then the corresponding linear equation is $2x+3y=12$

When x=0, we have $2*0+3y=12$

$\implies 3y=12\implies y=4$

When y=0, we have $2x+3*0=12$

$\implies 2x=12\implies x=6$

The T-table is:

0 | 4

6 | 12

We plot this points and draw a solid straight line as shown in the attachment.

Now let us test the origin: (0,0) by plugging x=0 and y=0 into the inequality.

$2*0+3*0\le12$

$0\le12$ ....This is true so we shade the lower half plane as shown in the attachment.

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3 years ago

A student organization wondered how many hours per week college students study during a term. Each of the 10 students in the org

Inga [223]

Answer:

No, a convenience sample was taken.Therefore, the sample may not be representative of all college students in terms of number of hours studied per week.

Step-by-step explanation:

One of the important conditions required in other to estimate the mean of the population from the confidence interval. Requires that the data must be a random Sample. This is to ensure that sample values are not biased and as such are representative of the larger group of data.

However, in the scenario described above, the sample chose. Are friend's of the student, this makes the data lack randomness as those who aren't friends to the student do not stand a chance of being selected. The sampling procedure employed is called convenience sampling.

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3 years ago

Your aunt is asking your help in figuring out how to

Marizza181 [45]

Answer:

650

Step-by-step explanation:

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3 years ago

Find the value of x in the figure below. (7x 17) (8x+ 2)

katrin2010 [14]

Hope this helps! I have to type more words apparently for me to send this. Ok that should work!