Solve the equation |5x+3|-3=3

Mathematics

1 answer:

arlik [135]4 years ago

6 0

Answer:

Step-by-step explanation:

Solve for

by simplifying both sides of the equation, then isolating the variable.

Exact Form:

−

Decimal Form:

0.6

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1.8

Mixed Number Form:

−

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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

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