Mathematics: Limit question: lim x-- pi ((e^sinx)-1)/(x-pi)

Limit question: lim x-- pi ((e^sinx)-1)/(x-pi)

Ответ:

cbwarner1325

02.01.2022

$\displaystyle\lim_{x\to\pi}\dfrac{e^{\sin x}-1}{x-\pi}$

Notice that if $f(x)=e^{\sin x}$ , then $f(\pi)=e^{\sin\pi}=e^0=1$ . Recall the definition of the derivative of a function f(x)

at a point x=c

:

$f'(c):=\displaystyle\lim_{x\to c}\frac{f(x)-f(c)}{x-c}$

So the value of this limit is exactly the value of the derivative of $f(x)=e^{\sin x}$ at $x=\pi$ .

You have

$f'(x)=\cos x\,e^{\sin x}\implies f'(\pi)=\cos\pi\,e^{\sin\pi}=-1$

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Ответ:

isabellatessa86

20.06.2022

Mathematics

Answer; Mean = p = 0.75

Standard deviation =0.0274

Step-by-step explanation:

Mean = p = 0.75

Standard deviation = √ [ p ( 1 - p) / n ]

= √ [ 0.75 * ( 1 - 0.75) / 250]

= 0.0274

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Limit question: lim x--> pi ((e^sinx)-1)/(x-pi)

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