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kiruha [24]
3 years ago
7

Question 8 of 10

Mathematics
2 answers:
nadezda [96]3 years ago
8 0
The answer is 8, I worked it all out…
german3 years ago
7 0

Answer:

I believe 8

Step-by-step explanation:

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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
Enter a phrase for the expression
Nina [5.8K]

Answer:

The quotient of x and 11.

Step-by-step explanation:

Given:

\frac{x}{11}

Required:

Write the expression in words

Solution:

In the expression given, we have the numerator which is the dividend (x), and the denominator which is the divisor (8).

So, we are dividing x into 8 parts.

A quotient is the result you get when you divide the dividend by the divisor.

✅In describing the expression in words, we would use the following phrase:

The quotient of x and 11.

The dividend is mentioned first before the dividend.

8 0
2 years ago
Basic algebra question I struggle with
maxonik [38]
Cross multiply
2x(3x-4) = 3(x+2)
5x - 8x = 3x + 6 
-3x= 3x+6
x = 6
I think 
5 0
3 years ago
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Can someone help mee :(((?
Shkiper50 [21]

Step-by-step explanation:

2√48= 13.86

3√147= 36.37

Perimeter: 13.86+13.86+36.37+36.37= 100.46

4 0
3 years ago
What happens to the value of f(x) = log4x as x approaches +∞?
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f(x) approaches infinity

I just took it on e2020!

8 0
3 years ago
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