asinus

Hello IronDome!

Does f(x) = sin1/x have a tangent line at x=0. Explain why or why not.

You mean f(x) = sin (1/x) ?

f(x) = sin (1/x) = sin (x ^-1)

f'(x) = cos (1/x) * (- 1/x²)

There is no tangent.  1 / (x = 0) and (-1/(x=0)²) is not defined.

1/0 is not defined.

Greeting asinus :- )

   !

Hello Guest!

What is the slope of a line that is perpendicular to

the line that passes through the points P1 (4, 7) and P2 (9, 3)?

m1 \( = \frac{y2 -x2}{y1-x1} \)

\(m1 = \frac{3- 9}{7- 4} \)

m1 = - 2

The slope of the perpendicular function is the

negative reciprocal of the slope of the output function.

m2 = - 1 / m1

\(m2 = \frac{- 1}{-2} = \frac{1}{2} \)

The slope of the perpendicular function is

\(m2 = \frac{1}{2} \)

Greeting asinus :- )

   !

Hello Guest!

Which is linear

f(x) = (1/2)2x

or

f(x) = -1/2 (x-2) ?

f(x) = (1/2)2x

\(f(x) = \frac{1}{2}\times 2x \)

f(x) = x

f(x) is linear                      a straight {nl}  

f(x) = -1/2 (x-2)

\(f(x)= \frac{-1}{2(x-2)} \)

\(f(x) = \frac{ 1}{ 4- 2x}\)

f (x) is non-linear             a hyperbola {nl}  

Greeting asinus :- )

  !

Hallo Gast!

Wie viele Minuten entsprechen 0,8 Stunden?

0,8 h * 60 min / h = 48 min

Das ist der Rechenweg.

Gruß asinus :- )

   !

I have calculated myself on the top line.
Sorry!

Hello Max!

\(\text{What's } (x+\frac{1}{x})^4 \text{ ?}\) 

\( (x+\frac{1}{x})^4 \)  = \((x^{2} + \frac{x}{2} + \frac{1}{x^{2} })^{2} \) 

^{\(= x^{4} + \frac{x^{3} }{2}+ 1 + \frac{x^{3} }{2}+\frac{x^{2} }{4} + \frac{1}{2x}+ 1 + \frac{1}{2x}+ \frac{1}{x^{4} } \)}

^{\(= x^{4}+ x^{3} + 2+ \frac{x^{2} }{4} + x+ \frac{1}{x^{4} } \)}

Greeting asinus :- )

   !

Guten Abend Gast!

Wie groß ist der Durchmesser eines Kreises dessen Umfang 1 km ist?

Der Umfang eines Kreises ist

\(U= d\times \pi \)

Der Durchmesser ist

\(d= \frac{U}{\pi } \) 

U = 1000 m

\(d= \frac{1000\ m}{\pi } \)

\(d= 318,310\ m \)

Der Durchmesser eines Kreises vom Umfang U = 1 km

ist d = 318,310 m.

Gruß asinus :- )

   !

Hallo geno and Alan!

An equation

How many real roots does it have:

\(|\frac{1}{x}-\frac{2}{x+1}|=\frac{2}{x}\)

a)Exactly 3 real roots

b)Exactly 2 real roots

c)Exactly 1 real root

d)It doesn't have any real roots

Of course you are right.
The condition "abs" matters:
Without "absolutely" is x = - 1/3,
with the "absolutely" no root.

It applies
d) It does not have any real roots

Greeting asinus :- )

   !

Hallo Guest!

An equation

How many real roots does it have:

\(|\frac{1}{x}-\frac{2}{x+1}|=\frac{2}{x}\)

a)Exactly 3 real roots

b)Exactly 2 real roots

c)Exactly 1 real root

d)It doesn't have any real roots

\(|\frac{1}{x}-\frac{2}{x+1}|=\frac{2}{x}\)

\(\frac{x+1-2x}{x²+x}= \frac{2x+2}{x²+x} \)                                  [ * ( x² + x)

x + 1 - 2x = 2x + 2

- 3x = 1

x = - 1 / 3

Sample:

1 / (- 1 / 3) - 2 / (1 - 1 / 3) = 2 / (- 1 / 3)

       - 3      -              3       =   - 6

                                     - 6 = - 6

c)Exactly 1 real root

Greeting asinus :- )

   !

Hello guest1 and guest2 !

2x+5x=25x

2x+5x=25x

18x = 0        [ / 6

3 * x = 0

x = 0

Sample:

3 * x = 0

3 * 0 = 0

0 = 0

"Three times zero is zero remains zero ..."

"Drei mol Null is Null bliev Null"

For this, a song from Cologne on the Rhine:

"Drei mol Null is Null bliev Null..."