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3 years ago

( 20 points ) The following table represents the function h(x)... Complete the table for

Mathematics

1 answer:

valina [46]3 years ago

3 0

Answer:

see the procedure

Step-by-step explanation:

we have that

$g(x)=\frac{1}{2}h(x)$

we know that

To obtain the value of g(x), multiply the value of h(x) by one-half

1) For x=-4, h(x)=256

$g(x)=\frac{1}{2}(256)=128$

therefore

For x=-4, g(x)=128

2) For x=-2, h(x)=16

$g(x)=\frac{1}{2}(16)=8$

therefore

For x=-2, g(x)=8

3) For x=0, h(x)=0

$g(x)=\frac{1}{2}(0)=0$

therefore

For x=0, g(x)=0

4) For x=3, h(x)=81

$g(x)=\frac{1}{2}(81)=40.5$

therefore

For x=3, g(x)=40.5

5) For x=6, h(x)=1296

$g(x)=\frac{1}{2}(1296)=648$

therefore

For x=6, g(x)=648

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Consider the function f(x)=xln(x). Let Tn be the nth degree Taylor approximation of f(2) about x=1. Find: T1, T2, T3. find |R3|

Fynjy0 [20]

Answer:

R3 <= 0.083

Step-by-step explanation:

f(x)=xlnx,

The derivatives are as follows:

f'(x)=1+lnx,

f"(x)=1/x,

f"'(x)=-1/x²

f^(4)(x)=2/x³

Simialrly;

f(1) = 0,

f'(1) = 1,

f"(1) = 1,

f"'(1) = -1,

f^(4)(1) = 2

As such;

T1 = f(1) + f'(1)(x-1)

T1 = 0+1(x-1)

T1 = x - 1

T2 = f(1)+f'(1)(x-1)+f"(1)/2(x-1)^2

T2 = 0+1(x-1)+1(x-1)^2

T2 = x-1+(x²-2x+1)/2

T2 = x²/2 - 1/2

T3 = f(1)+f'(1)(x-1)+f"(1)/2(x-1)^2+f"'(1)/6(x-1)^3

T3 = 0+1(x-1)+1/2(x-1)^2-1/6(x-1)^3

T3 = 1/6 (-x^3 + 6 x^2 - 3 x - 2)

Thus, T1(2) = 2 - 1

T1(2) = 1

T2 (2) = 2²/2 - 1/2

T2 (2) = 3/2

T2 (2) = 1.5

T3(2) = 1/6 (-2^3 + 6 *2^2 - 3 *2 - 2)

T3(2) = 4/3

T3(2) = 1.333

Since;

f(2) = 2 × ln(2)

f(2) = 2×0.693147 =

f(2) = 1.386294

Since;

f(2) >T3; it is significant to posit that T3 is an underestimate of f(2).

Then; we have, R3 <= | f^(4)(c)/(4!)(x-1)^4 |,

Since;

f^(4)(x)=2/x^3, we have, |f^(4)(c)| <= 2

Finally;

R3 <= |2/(4!)(2-1)^4|

R3 <= | 2 / 24× 1 |

R3 <= 1/12

R3 <= 0.083

5 0

3 years ago

If two lines intersect, then their intersection is exactly one point. ...draw a sketch to illustrate

Lostsunrise [7]

Just sketch two lines crossing each other like a street intersection.

4 0

3 years ago

Given the following formula, solve for h.<br> <img src="https://tex.z-dn.net/?f=%20V%3D%20%5Cfrac%7B1%7D%7B3%7D%20%5Cpi%20r%5E%7

IgorC [24]

Multiply by the inverse of the coefficient of h.

$h=\dfrac{3V}{\pi r^2}$

3 0

3 years ago

Read 2 more answers

A contractor is calculating the number of decorative stones for a new rectangular patio. The bids always include a count for the

babunello [35]

Answer:

The number of edge stones needed has a constant rate of change, but the number of stones for the center does not.

Step-by-step explanation:

The complete question is shown in the picture attached below.

Two functions E(x) and C(x) are given in the table along with some of the function values. We have to identify if any of these functions show constant rate of change or not.

By constant rate of change we mean that the slope is constant or in other words, a linear relationship is shown by the function. For a Linear function, the first differences of the function values are same.

By first differences we mean the difference between two consecutive output values. We can see that difference between consecutive input values is constant i.e. 1. If the difference between consecutive output values of any of the functions is same, then that function will be a Linear Function and, therefore, the rate of change for that function will be constant.

Lets analyze E(x) first. The output values are:

34, 52, 70 and 88

The difference between consecutive output values is:

18, 18 and 18

Since, this difference is constant, we can conclude that E(x) is a Linear function with a constant rate of change.

Now lets analyze C(x). The output values are:

62, 133, 260 and 435

The difference between consecutive output values is:

71, 127 and 175

Since, the differences are not constant, C(x) is not a Linear Function and , therefore, the rate of change of C(x) is not constant.

Conclusion:

The number of edge stones which is represented by E(x) has a constant rate of change, but the number of stones for center which is represented by C(x) does not have constant rate of change. This makes the first option our correct answer.

3 0

3 years ago

7y + 4x - 10 + 5y - 5 + x

Lemur [1.5K]

Answer:

hope it helps u

Step-by-step explanation:

7y + 4x - 10 + 5y - 5 + x

= 7y+5y+4x+x–10–5

= 12y+5x–15

7 0

3 years ago

Read 2 more answers