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Fed [463]
2 years ago
13

Use fundamental theorem of calculus to find derivative of the function LOOK AT PHOTO

Mathematics
1 answer:
kykrilka [37]2 years ago
8 0

Let c > 0. Then split the integral at t = c to write

f(x) = \displaystyle \int_{\ln(x)}^{\frac1x} (t + \sin(t)) \, dt = \int_c^{\frac1x} (t + \sin(t)) \, dt - \int_c^{\ln(x)} (t + \sin(t)) \, dt

By the FTC, the derivative is

\displaystyle \frac{df}{dx} = \left(\frac1x + \sin\left(\frac1x\right)\right) \frac{d}{dx}\left[\frac1x\right] - (\ln(x) + \sin(\ln(x))) \frac{d}{dx}\left[\ln(x)\right] \\\\ = -\frac1{x^2} \left(\frac1x + \sin\left(\frac1x\right)\right) - \frac1x (\ln(x) + \sin(\ln(x))) \\\\ = -\frac1{x^3} - \frac{\sin\left(\frac1x\right)}{x^2} - \frac{\ln(x)}x - \frac{\sin(\ln(x))}x \\\\ = -\frac{1 + x\sin\left(\frac1x\right) + x^2\ln(x) + x^2 \sin(\ln(x))}{x^3}

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gladu [14]

Answer:

80

Step-by-step explanation:

-4f(x)=-12x+44

-4f(-3)=36+44=80

6 0
3 years ago
What is the simplified form of √144x^36
Nadusha1986 [10]

Answer:

The simplified form of \sqrt{144x^{36}} is 12x^{18}

Step-by-step explanation:

Given : \sqrt{144x^{36}}

We have to write the simplified form of \sqrt{144x^{36}}

Consider the given expression \sqrt{144x^{36}}

We know \sqrt{144}=12

and \sqrt{x^{36}}=\sqrt{x^{18}\cdot x^{18}}

Thus,

\sqrt{144x^{36}}=\sqrt{12^2\cdot (x^{18})^2}

Simplify, we have,

=\sqrt{12^2\cdot (x^{18})^2}=12x^{18}

Thus, The simplified form of \sqrt{144x^{36}} is 12x^{18}

6 0
3 years ago
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5. The point (-7, 4) is reflected over the line x = -3. Then,
Genrish500 [490]

Answer:

(4,1)

Step-by-step explanation:

Reflected over x = -3, new point : (1,4)

Reflected over y=x, new point = (4,1)

6 0
2 years ago
What is the answer <br><br> 3<br> x −4=−8
Artyom0805 [142]

Step-by-step explanation:

3x-4=-8

3x=-8+4

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2 years ago
What makes two angles exterior versus interior ?<br>​
astraxan [27]

Answer:

Any angle that is on the inside of a shape is called an interior angle.

Step-by-step explanation:

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