Find the domain for 5/x2-9

Mathematics

1 answer:

Viktor [21]3 years ago

4 0

Answer:

x > -3 or -3 < x < 3 or x > 3

Step-by-step explanation:

$x^{2}$ - 9

= (x + 3)(x - 3)

the undefined singularity points are at x = 3 and x = -3

x > 3 or x > -3

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Question 5

baherus [9]

9514 1404 393

Answer:

A. no solution

Step-by-step explanation:

The solution is found where the lines meet. Parallel lines never meet, so there is no solution.

7 0

3 years ago

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

aleksandr82 [10.1K]

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

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

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