Is 787887888.. a rational number?

Mathematics

1 answer:

lisabon 2012 [21]3 years ago

3 0

Answer:

kpk

Step-by-step explanation:

knkn

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How to write 438 in standard

Anton [14]

400+30+8 is how you put 438 in standard form.

8 0

3 years ago

Read 2 more answers

If f (n)(0) = (n + 1)! for n = 0, 1, 2, , find the taylor series at a=0 for f.

Pie

Given that $f^{(n)}(0)=(n+1)!$ , we have for $f(x)$ the Taylor series expansion about 0 as

$f(x)=\displaystyle\sum_{n=0}^\infty\frac{(n+1)!}{n!}x^n=\sum_{n=0}^\infty(n+1)x^n$

Replace $n+1$ with $n$ , so that the series is equivalent to

$f(x)=\displaystyle\sum_{n=1}^\infty nx^{n-1}$

and notice that

$\displaystyle\frac{\mathrm d}{\mathrm dx}\sum_{n=0}^\infty x^n=\sum_{n=1}^\infty nx^{n-1}$

Recall that for $|x|$ , we have

$\displaystyle\sum_{n=0}^\infty x^n=\frac1{1-x}$

which means

$f(x)=\displaystyle\sum_{n=1}^\infty nx^{n-1}=\frac{\mathrm d}{\mathrm dx}\frac1{1-x}$
$\implies f(x)=\dfrac1{(1-x)^2}$

5 0

3 years ago

10. A 266-hp output is required for an engine. If there is a 5% loss of power, what amount of input

marta [7]

Answer:

Amount of input horsepower needed is 279.3 hp.

Step-by-step explanation:

if there is a loss of power of 5% the base horsepower will need to be increased by same percentage so that same amount of power can be delivered.

Now to calculate 5% of 266 hp, we can write

266 × $\frac{5}{100}$ = 13.3 hp