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3 years ago

Please help I’m timed

Mathematics

2 answers:

kipiarov [429]3 years ago

8 0

Answer:

AA5

Step-by-step explanation:

liubo4ka [24]3 years ago

6 0

SAS is the correct answer

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Derivative of tan(2x+3) using first principle

kodGreya [7K]

$f(x)=\tan(2x+3)$

The derivative is given by the limit

$f'(x)=\displaystyle\lim_{h\to0}\frac{f(x+h)-f(x)}h$

You have

$\displaystyle\lim_{h\to0}\frac{\tan(2(x+h)+3)-\tan(2x+3)}h$
$\displaystyle\lim_{h\to0}\frac{\tan((2x+3)+2h)-\tan(2x+3)}h$

Use the angle sum identity for tangent. I don't remember it off the top of my head, but I do remember the ones for (co)sine.

$\tan(a+b)=\dfrac{\sin(a+b)}{\cos(a+b)}=\dfrac{\sin a\cos b+\cos a\sin b}{\cos a\cos b-\sin a\sin b}=\dfrac{\tan a+\tan b}{1-\tan a\tan b}$

By this identity, you have

$\tan((2x+3)+2h)=\dfrac{\tan(2x+3)+\tan2h}{1-\tan(2x+3)\tan2h}$

So in the limit you get

$\displaystyle\lim_{h\to0}\frac{\dfrac{\tan(2x+3)+\tan2h}{1-\tan(2x+3)\tan2h}-\tan(2x+3)}h$
$\displaystyle\lim_{h\to0}\frac{\tan(2x+3)+\tan2h-\tan(2x+3)(1-\tan(2x+3)\tan2h)}{h(1-\tan(2x+3)\tan2h)}$
$\displaystyle\lim_{h\to0}\frac{\tan2h+\tan^2(2x+3)\tan2h}{h(1-\tan(2x+3)\tan2h)}$
$\displaystyle\lim_{h\to0}\frac{\tan2h}h\times\lim_{h\to0}\frac{1+\tan^2(2x+3)}{1-\tan(2x+3)\tan2h}$
$\displaystyle\frac12\lim_{h\to0}\frac1{\cos2h}\times\lim_{h\to0}\frac{\sin2h}{2h}\times\lim_{h\to0}\frac{\sec^2(2x+3)}{1-\tan(2x+3)\tan2h}$

The first two limits are both 1, and the single term in the last limit approaches 0 as $h\to0$ , so you're left with

$f'(x)=\dfrac12\sec^2(2x+3)$

which agrees with the result you get from applying the chain rule.

7 0

3 years ago

Is this the correct answer? Please someone help!!!

Whitepunk [10]

Answer:

yes

Step-by-step explanation:

same slope

3 0

3 years ago

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Vlada [557]

You can make about 11 burgers with that

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Given a situation involving a dilation, how do you determine the scale factor.

USPshnik [31]

Answer:

See explanation below.

Step-by-step explanation:

The scale factor can be found by dividing two corresponding side lengths. For instance, if you have two triangles, divide the new length of the larger or smaller triangle by the same side length of the original.

If the side length of the new was 9 and the old was 3 then the scale factor would be 9/3 = 3.

If it were flipped then the new would be 3 and the old would be 9. So the scale factor would be 3/9 = 1/3.

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Find all roots of the polynomial function F(x)=x^2-2x-24

liq [111]

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3 years ago

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