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Dimas [21]
3 years ago
7

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

Mathematics
1 answer:
aleksandr82 [10.1K]3 years ago
4 0
\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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Anni [7]

Answer:

a) = 4.5

b) = 3.3

Step-by-step explanation:

Before solving our problems given to us let us under stand the rule of cube roots

It says \sqrt[3]{x \times x \times x} = x   -----(A)

Also

\sqrt[3]{x \times x \times x \times y \times y \times y} = x \times y   ---(B)

Now let us see each part one by one

a) we have

\sqrt[3]{64} + \sqrt[3]{0.027} + \sqrt[3]{0.008}

Now 64 = 4 x 4 x 4

0.027 = 0.3 x 0.3 x 0.3

0.008 = 0.2 x 0.2 x 0.2

substituting these values

\sqrt[3]{4 \times 4 \times 4} + \sqrt[3]{0.3 \times 0.3 \times 0.3} + \sqrt[3]{0.2 \times 0.2 \times 0.2}

Applying Rule A in above

=4+0.3+0.2

=4+0.5

4.5

b) we have \sqrt[3]{0.3 \times 0.3 \times 0.3 \times 11 \times 11 \times 11}

Applying the B rule in this

=0.3 \times 11

3.3

4 0
3 years ago
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vova2212 [387]

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Step-by-step explanation:

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Answer:

The ans is 3,4,5

Step-by-step explanation:

Hope it helps you Tq

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Step-by-step explanation:

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