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2 years ago

| x | < 2 solve the inequality and then graph the solution

Mathematics

1 answer:

anzhelika [568]2 years ago

3 0

Answer:

Any number smaller than 2

Step-by-step explanation:

You would graph this by wrighting a solid, filled in circle with an arrow point toward the negative numbers, because those numbers are smaller than 2

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Differentiate x^2 e^x logx

zimovet [89]

Product rule:

$\dfrac{\mathrm d}{\mathrm dx}(x^2e^x\log x)$

$=\dfrac{\mathrm d(x^2)}{\mathrm dx}e^x\log x+x^2\dfrac{\mathrm d(e^x)}{\mathrm dx}\log x+x^2e^x\dfrac{\mathrm d(\log x)}{\mathrm dx}$

Power rule:

$\dfrac{\mathrm d(x^2)}{\mathrm dx}=2x$

The exponential function is its own derivative:

$\dfrac{\mathrm d(e^x)}{\mathrm dx}=e^x$

Assuming the base of $\log x$ is $e$ , its derivative is

$\dfrac{\mathrm d(\log x)}{\mathrm dx}=\dfrac1x$

But if you mean a logarithm of arbitrary base $b$ , we have

$y=\log_bx\implies x=b^y=e^{y\ln b}\implies1=e^{y\ln b}\ln b\dfrac{\mathrm dy}{\mathrm dx}$

$\implies\dfrac{\mathrm dy}{\mathrm dx}=\dfrac{e^{-y\ln b}}{\ln b}=\dfrac1{b^y\ln b}$

$\implies\dfrac{\mathrm d(\log_bx)}{\mathrm dx}=\dfrac1{x\ln b}$

So we end up with

$2xe^x\log x+x^2e^x\log x+\dfrac{x^2e^x}x$

$=xe^x(2\log x+x\log x+1)$

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3 years ago

There are fifteen teams in a high school baseball league. How many different orders of finish are possible for the first four p

ankoles [38]

There are 32,760 different orders for the first four positions.

This is a permutation where repetition is not allowed; the formula for that is:

$_nP_r=\frac{n!}{(n-r)!}$

For our problem, we have:
$_{15}P_4=\frac{15!}{(15-4)!}=\frac{15!}{11!}=32760$

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3 years ago

1 of 6

nasty-shy [4]

Answer:

something

Step-by-step explanation:

sry i need answers

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3 years ago

A water park charges $5 for entry into the park and an additional $2 for each of the big water slides. Steven spent $17 on his v

morpeh [17]

LET X= ADDITIONAL AMOUNT
<u>EQAUTION=</u> 5+2x=17
-5 -5
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3 years ago

Read 2 more answers

I need help pls explain

vladimir1956 [14]

For 1. The bike is going 24 miles in 3 hours. To figure out how many miles it went in 1 hour you divide 24/3 which is 8 miles. If the bike went 8 miles per hour then you may now multiply it by 10 to find the total mileage in 10 hours. 10x8=80

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3 years ago