Samirs bedroom has an area of 48 square feet.

Use series to verify that<br><br> <img src="https://tex.z-dn.net/?f=y%3De%5E%7Bx%7D" id="TexFormula1" title="y=e^{x}" alt="y=e^{

SVETLANKA909090 [29]

$y = e^x\\\\\displaystyle y = \sum_{k=1}^{\infty}\frac{x^k}{k!}\\\\\displaystyle y= 1+x+\frac{x^2}{2!} + \frac{x^3}{3!}+\ldots\\\\\displaystyle y' = \frac{d}{dx}\left( 1+x+\frac{x^2}{2!} + \frac{x^3}{3!}+\frac{x^4}{4!}+\ldots\right)\\\\$

$\displaystyle y' = \frac{d}{dx}\left(1\right)+\frac{d}{dx}\left(x\right)+\frac{d}{dx}\left(\frac{x^2}{2!}\right) + \frac{d}{dx}\left(\frac{x^3}{3!}\right) + \frac{d}{dx}\left(\frac{x^4}{4!}\right)+\ldots\\\\\displaystyle y' = 0+1+\frac{2x^1}{2*1} + \frac{3x^2}{3*2!} + \frac{4x^3}{4*3!}+\ldots\\\\\displaystyle y' = 1 + x + \frac{x^2}{2!}+ \frac{x^3}{3!}+\ldots\\\\\displaystyle y' = \sum_{k=1}^{\infty}\frac{x^k}{k!}\\\\\displaystyle y' = e^{x}\\\\$

This shows that $y' = y$ is true when $y = e^x$

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Note 1: A more general solution is $y = Ce^x$ for some constant C.
Note 2: It might be tempting to say the general solution is $y = e^x+C$ , but that is not the case because $y = e^x+C \to y' = e^x+0 = e^x$ and we can see that $y' = y$ would only be true for C = 0, so that is why $y = e^x+C$ does not work.

6 0

3 years ago

Which function has a domain of all real numbers except x=π/2 ±nπ?

boyakko [2]

<span>A. y=secx This problem deals with the various trig functions and is looking for those points where they are undefined. Since the only math operations involved is division, that will happen with the associated trig function attempts to divide by zero. So let's look at the functions that are a composite of sin and cos. sin and cos are defined for all real numbers and range in value from -1 to 1. sin is zero for all integral multiples of pi, and cos is zero for all integral multiples of pi plus pi over 2. So the functions that are undefined will be those that divide by cos. tan = sin/cos, which will be undefined for x = π/2 ±nπ cot = cos/sin, which will be undefined for x = ±nπ sec = 1/cos, which will be undefined for x = π/2 ±nπ csc = 1/sin, which will be undefined for x = ±nπ Now let's look at the options and pick the correct one. A. y=secx * There's a division by cos, so this is the correct choice. B. y=cosx * cos is defined over the entire domain, so this is a bad choice. C. y=1/sinx * The division is by sin, not cos. So this is a bad choice. D. y=cotx, * The division is by sin, not cos. So this is a bad choice.</span>

4 0

3 years ago

Sierra has plotted two vertices of a rectangle at (3,2) and (8,2). What is the length of the sides of the rectangle

Eddi Din [679]

Answer:

5units

Step-by-step explanation:

Given the two vertices of a rectangle at (3,2) and (8,2). We are to calculate the distance between the two points.

Using the formula

D = √(x2-x1)²+(y2-y1)²

D = √(2-2)²+(8-3)²

D = √0+5²