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3 years ago

Please help! It’s for a test, I’ll also give brainliest!

Mathematics

1 answer:

wolverine [178]3 years ago

4 0

True
Because 9 is a odd number as of 1,3,5 are

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Evaluate the limit as x approaches 0 of (1 - x^(sin(x)))/(x*log(x))

e-lub [12.9K]

$sin~ x \approx x ~ ~\sf{as}~~ x \rightarrow 0$

We can replace sin x with x anywhere in the limit as long as x approaches 0.

Also,

$\large \lim_{ x \to 0 } ~ x^x = 1$

I will make the assumption that log(x)=ln(x).

The limit result can be proven if the base of log(x) is 10.

$\large \lim_{x \to 0^{+}} \frac{1- x^{\sin x} }{x \log x } \\~\\ \large = \lim_{x \to 0^{+}} \frac{1- x^{\sin x} }{ \log( x^x) } \\~\\ \large = \lim_{x \to 0^{+}} \frac{1- x^{x} }{ \log( x^x) } ~~ \normalsize{\text{ substituting x for sin x } } \\~\\ \large = \frac{\lim_{x \to 0^{+}} (1) - \lim_{x \to 0^{+}} \left( x^{x}\right) }{ \log( \lim_{x \to 0^{+}}x^x) } = \frac{1-1}{\log(1)} = \frac{0}{0}$

We get the indeterminate form 0/0, so we have to use Lhopitals rule

 $\large \lim_{x \to 0^{+}} \frac{1- x^{x} }{ \log( x^x) } =_{LH} \lim_{x \to 0^{+}} \frac{0 -x^x( 1 + \log (x)) }{1 + \log (x) } \\ = \large \lim_{x \to 0^{+}} (-x^x) = \large - \lim_{x \to 0^{+}} (x^x) = -1$

Therefore,

 $\large \lim_{x \to 0^{+}} \frac{1- x^{\sin x} }{x \log x } =\boxed{ -1}$

3 0

3 years ago

If you’re good at algebra could somebody help me please?

Mama L [17]

Answer:

a). f(0) = 7

b). f( $\frac{1}{3}$ ) = 6

c). f(-5) = 22

d). x = 9

Step-by-step explanation:

The given function is f(x) = -3x + 7

a). For x = 0

f(0) = -3(0) + 7

= 0 + 7

= 7

b). For x = $\frac{1}{3}$

f( $\frac{1}{3}$ ) = $(-3)(\frac{1}{3})+7$

= -1 + 7

= 6

c). For x = (-5)

f(-5) = -3(-5) + 7

= 15 + 7

= 22

d). For f(x) = (-20)

-20 = -3x + 7

3x = 20 + 7

3x = 27

x = 9

3 0

3 years ago

PLS HELP! - x + 4y = -9 y = -2x + 6 Is (2,3) a solution of the system?

skelet666 [1.2K]

Answer is no!!!
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3 years ago

Solve with k=10. Remember Oder of operations! 5k2

luda_lava [24]

Answer:

510*510

=5102

=260100

5(10)^2

5*100 = 500

7 0

3 years ago

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Given the points (5, 4) and (-3, 2), find the slope of a line that passes through both points.

mr Goodwill [35]

-11 ................

7 0

3 years ago