In case you're not already aware, the expression $\frac{f(x+h)-f(x)}h$ is called the "difference quotient" and represents the average rate of change of a function $f$ over an interval $[x,x+h]$ .

For the function $f(x)=x^2+3x+4$ , by substituting $x+h$ we get

$f(x+h)=(x+h)^2+3(x+h)+4=(x^2+2xh+h^2)+(3x+3h)+4=x^2+3x+4+(2x+3)h+h^2$

Then the difference quotient is

$\dfrac{f(x+h)-f(x)}h=\dfrac{(x^2+3x+4+(2x+3)h+h^2)-(x^2+3x+4)}h$

$=\dfrac{(2x+3)h+h^2}h=2x+3+h$

where the last equality holds as long as $h\neq0$ .

5 0

3 years ago

Which classification describes the following syastem of equations? x=5 y=6 -x - y +z = 0

Papessa [141]

Answer:

Is a consistent independent system

Step-by-step explanation:

we know that

If a system has at least one solution, it is said to be consistent .

If a consistent system has exactly one solution, it is independent .

If a consistent system has an infinite number of solutions, it is dependent

If a system not have solution, it is said to be inconsistent

we have

$x=5$ ----> equation A

$y=6$ ----> equation B

$-x-y+z=0$ ----> equation C

substitute equation A and equation B in equation C

$-5-6+z=0$

Solve for z

$z=11$

The solution is the point (5,6,11)

The system has only one solution

therefore

Is a consistent independent system

6 0

3 years ago

What is the product of 7/10×(-9)

Andrews [41]

Answer:

-6.3

Step-by-step explanation:

7/10 X -9/1 = -63/10 = -6.3

4 0

2 years ago

Convert the fraction 7 24 into a repeating decimal.

goldenfox [79]

$\dfrac7{24}=\dfrac6{24}+\dfrac1{24}=\dfrac14+\dfrac1{24}$

$\dfrac1{24}=\dfrac1{8\time3}=\dfrac a8+\dfrac b3=\dfrac{3a+8b}{24}$
$\implies3a+8b=1$

We can choose $a=-1$ and $b=\dfrac12$ , so that

$\dfrac1{24}=-\dfrac18+\dfrac16$

Recalling that $\dfrac13=0.333\ldots$ , it follows that $\dfrac16=0.166\ldots$ . So,

$\dfrac1{24}=0.125+0.166\ldots=0.04166\ldots$
$\implies\dfrac7{24}=0.25+0.4166\ldots=0.29166\ldots$

6 0

2 years ago