3 years ago

Someone EXPLAIN HOW + dont just answer!! i need an explanation and an answer

Mathematics

1 answer:

sdas [7]3 years ago

7 0

Answer:

< - 5, 3.5 >

Step-by-step explanation:

A single translation is required to map A onto B

Consider the point (5, 3 ) on A and the corresponding point (0, 6.5) on B

the translation is < 0 - 5, 6.5 - 3 > = < - 5, 3.5 >

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

kykrilka [37]

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

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