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3 years ago

Given that g(x)=x^2, find each of the following.

1 answer:

8 0

G(x) = x²
a) To find g(1) substitute with x = 1 at the function g(x)
∴ g(1) = 1² = 1

b) substitute with x = -2 at the function g(x)
∴ g(-2) = (-2)² = 4

c) substitute with x = -x at the function g(x)
∴ g(-x) = (-x)² = x²

d) substitute with x = 2y at the function g(x)
∴ g(2y) = (2y)² = 4y²

e) substitute with x = 2+h at the function g(x)
∴ g(2+h) = (2+h)² = h² + 4h + 4

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F(x) = lnx/x

My name is Ann [436]

$f(x) = \frac{lnx}{x}$

(a) $f'(x) = \frac{d}{dx}[\frac{lnx}{x}]$
Using the quotient rule:
$f'(x) = \frac{\frac{1}{x} \cdot x - lnx}{x^{2}}$
$f'(x) = \frac{1 - lnx}{x^{2}}$

For maximum, f'(x) = 0;
$\frac{1 - lnx}{x} = 0$
$lnx = 1, x = e$

(b) <em>Deduce:
</em> $e^{x} \geq x^{e}, x > 0$
<em>
Soln:</em> Since x = e is the greatest value, then f(e) ≥ f(x) > f(0)
$\frac{ln(e)}{e} \geq \frac{lnx}{x}$
$\frac{1}{e} \geq \frac{lnx}{x}$ , since ln(e) is simply equal to 1

Now, since x > 0, then we don't have to worry about flipping the signs when multiplying by x.
$\frac{x}{e} \geq lnx$
$x \geq elnx$
$x \geq ln(x^{e})$

Taking the exponential to both sides will cancel with the natural logarithmic function in the right hand side to produce:
$e^{x} \geq e^{ln(x^{e}})$
$e^{x} \geq x^{e}$ , as required.

3 0

3 years ago

PLEASE HELP ASAP!!! (Directions: Find the surface area of the prism) #5.

topjm [15]

SA= bh+2ls+lw
SA= 26*10 +40*26(2)+40*10
SA=260+1040(2)+400
SA=260+2080+400
SA=2740

5 0

3 years ago

46 2/3% of 28 please i need to know answer an work

Bogdan [553]

First, it would help to put 46 and 2/3 into an improper fraction: 140/3.

Then, since this is a percent, we put that improper fraction over 100: (140/3)/100 = 140/300.

Finally, we multiply this answer by 28 since "of" means multiply:

(140/300) * 28 = 196/15 = 13 1/15

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3 years ago

What decimal can be added to 0.0(54) to get 0.1(54)? (the parenthesis mean repeating)

son4ous [18]

Add 0.1 to 0.0(54) to get 0.1(54).

5 0

3 years ago

Read 2 more answers

3. A family is tracking its spending habits. Over the past year, the grocery bill has ranged from $110 to $170. Suppose you were

ra1l [238]

You would plot them by month, 170-110= 60 dollar increase. 60 divided by 12 ( for each month) leaves a 5 dollar increase each month. Your coordinates would be 0,110 1,115 2,120 3,125
x would be month
y would be money

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3 years ago

Given that g(x)=x^2​, find each of the following.

Given that g(x)=x^2, find each of the following.