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3 years ago

Is 5y=x+ (1 over 3) proportional?

1 answer:

8 0

No.

The relation is proportional when it can be written as
y = kx

As soon as you add a constant, you destroy the proportionality.

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Evaluate the function at the given numbers( correct to six decimal places). Use the results to guess the value of the limit or e

netineya [11]

Answer:

Value of the limit is 0.5.

Step-by-step explanation:

Given,

$F(x)=\frac{e^x-1-x}{x^2}$

When,

$x=1,F(1)=frac{e^1-1-1}{1}=e-2=0.718281$

$x=0.5, F(0.5)=\frac{e^0.5-1-0.5}{(0.5)^2}=0.594885$

$x=0.1, F(0.1)=\frac{e^0.1-1-0.1}{(0.1)^2}=0.517091$

$x=0.05, F(0.05)=\frac{e^0.05-1-0.05}{(0.05)^2}=0.508438$

$x=0.01, F(0.01)=\frac{e^0.01-1-0.01}{(0.01)^2}=0.501670 \hfill (1)$

Correct upto six decimal places.

Now,

$\lim_{x\to 0}F(x)=\lim_{x\to 0}\frac{e^x-1-x}{x^2}$ $(\frac{0}{0})$ form, applying L-Hospital rule that is differentiating numerator and denominator we get,

$\lim_{x\to 0}F(x)$

$=\lim_{x\to 0}\frac{e^x-1}{2x}$ $(\frac{0}{0})$ form.

$=\lim_{x\to 0}\frac{e^x}{2}=\frac{1}{2}=0.5\hfill (2)$

Limit exist and is 0.5. That is according to (1) we can see as the value of x lesser than 1 and tending to near 0, value of the function decreases respectively. And from (2) it shows ultimately it decreases and reach at 0.5, consider as limit point of F(x).

8 0

3 years ago

two times a number is subtracted from 25 the result is the same as when it is added to six times.find the number

ExtremeBDS [4]

Answer:

6.3

Step-by-step explanation:

1. 25 - 2n = n + 6

2. 25 = 3n + 6

3. 3n = 19

4. n = 6.3

8 0

3 years ago

The scale on a map is 1cm=20miles.if two airports are 4cm apart on the map, what's the distance between the airports?

Stels [109]

80 miles because if 1=20 then 2=40 3=60 4=80

8 0

3 years ago

Help me please having trouble!?

nlexa [21]

2+2=4 2 X 2 = 4 2 X 3 = 6

5 0

3 years ago

James spent $(2y2 + 6). He bought notebooks that each cost $(y2 − 1).

CaHeK987 [17]

The expression to find the number of notebooks James bought would be written as:

Number of notebooks = total spent / cost per item

Number of notebooks = (2y^2 + 6) / (y^2 − 1)

If y = 3, then the number of notebooks bought would be:

Number of notebooks = (2y^2 + 6) / (y^2 − 1)
Number of notebooks = (2(3)^2 + 6) / (3^2 − 1)
Number of notebooks = 3 pieces

7 0

3 years ago