MATHEMATICS COLLEGE

Graph the following function and then find the specified limits. When necessary, state that the limit does not exist.f(x)equals=left brace Start 3 By 2 Matrix 1st Row 1st Column x minus 3 2nd Column if x less than 5 2nd Row 1st Column 2 2nd Column if 5 less than or equals x less than or equals 6 3rd Row 1st Column x plus 4 2nd Column if x greater than 6 EndMatrixx−3 if x<52 if 5≤x≤6x+4 if x>6;findModifyingBelow lim With x right arrow 5limx→5 f(x)andModifyingBelow lim With x right arrow 6limx→6 f(x)

Answers

Answer 1

Answer:

If I'm reading the question right, you have

$f(x)=\begin{cases}x-3&\text{for }x<5\n2&\text{for }5\le x\le6\nx+4&\text{for }x>6\end{cases}$

and you have to find

$\displaystyle\lim_(x\to5)f(x)\text{ and }\lim_(x\to6)f(x)$

The limits exist if the limits from either side exist. We have

$\displaystyle\lim_(x\to5^-)f(x)=\lim_(x\to5)(x-3)=2$

$\displaystyle\lim_(x\to5^+)f(x)=\lim_(x\to5)2=2$

$\implies\displaystyle\lim_(x\to5)f(x)=2$

and

$\displaystyle\lim_(x\to6^-)f(x)=\lim_(x\to6)2=2$

$\displaystyle\lim_(x\to6^+)f(x)=\lim_(x\to6)(x+4)=10$

$\implies\displaystyle\lim_(x\to6)f(x)\text{ does not exist}$

Answer 2

Answer:

Final answer:

The function f(x) is a piecewise function. The limit as x approaches 5 equals 2 and the limit as x approaches 6 does not exist as the values from both sides are not the same.

Explanation:

The function f(x) given is a piecewise function which is defined differently on different intervals of x.

First let's graph these three conditions:

For x < 5, f(x) = x - 3. It is a straight line that crosses the Y-axis at -3.
For 5 ≤ x ≤ 6, f(x) = 2. It is a horizontal line along the height of 2 from x=5 to x=6.
For x > 6, f(x) = x + 4. It is a straight line that crosses the Y-axis at 4.

Next, we'll find the specified limits:

limx→5 f(x): As x approaches 5, we will look at values from both sides. From the left (x < 5), it would be 5 - 3 = 2. From the right (5 ≤ x ≤ 6), f(x) = 2. The value is the same from both sides, so the limit as x approaches 5 equals 2.
limx→6 f(x): As x approaches 6, from the left (5 ≤ x ≤ 6), f(x) = 2. From the right (x > 6), it would be 6 + 4 = 10. The values are not the same from both sides, so the limit as x approaches 6 does not exist.

Learn more about Mathematical Limits here:

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(1) -3x - 4y + 11z from -9y + 6z - 3x

In order to make it easier for us to perform the required mathematical operations, we must first rearrange the terms in the subtrahend by alphabetical order.

-3x - 4y + 11z

-3x - 9y + 6z ⇒ This is the subtrahend.

Now, we can finally perform the subtraction on both trinomials:

$\displaystyle\mathsf{\left \ \quad\:\:\:\:{-3x - 4y + 11z} \atop -\quad{\underline{-3x - 9y + 6z\:\:\underline}} \right.}$

In the subtrahend, the coefficients of x and y are both negative. Thus, performing the subtraction operations on these coefficients transforms their sign into positive.

$\displaystyle\mathsf{\left \ \quad\:\:\:\:{-3x - 4y + 11z} \atop -\quad{\underline{-3x - 9y + 6z\:\:\underline}}\right.} \n\qquad\sf {\qquad\:\:\:0x\:+\:5y\:+5z$

The difference is: 5y + 5z.

(2) 3x⁴- 4x³ + 7x - 2 from 9 - 7x⁴ + 6x³- 2x² - 11x

Similar to the how we arranged the given trinomials in Question 1, we must rearrange the given polynomials in descending degree of terms before subtracting like terms.

3x⁴- 4x³ + 7x - 2 ⇒ Already in descending order (degree).

9 - 7x⁴ + 6x³- 2x² - 11x ⇒ -7x⁴ + 6x³- 2x² - 11x + 9

In subtracting polynomials, we can only subtract like terms, which are terms that have the same variables and exponents.

$\displaystyle\mathsf{\left \ \quad\:\:{3x^4\:-4x^3\:+\:0x^2\:+\:7x\:-\:2} \atop -\quad{\underline{-7x^4\:+6x^3\:-2x^2\:-11x\:+\:9 \:\:\underline}}\right.}$

In the minuend, I added the "0x²" to make it less-confusing for us to perform the subtraction operations.

The same rules apply in terms of coefficients with negative signs in the subtrahend, such as: -7x⁴, - 2x², and - 11x ⇒ their coefficients turn into positive when performing subtraction.

$\displaystyle\mathsf{\left \ \quad\:\:{3x^4\:-4x^3\:+\:0x^2\:+\:7x\:-\:2} \atop -\quad{\underline{-7x^4\:+6x^3\:-2x^2\:-11x\:+\:9 \:\:\underline}}\right.} \n\qquad\sf {\qquad\:\:10x^4-10x^3+2x^2+18x\:-11$

Therefore, the difference is: 10x⁴ - 10x³ + 2x² + 18x - 11.

Help me, please !! For a reason, Tony took 1/3 his money for book and then he took 1/5 again for beer. And now tony have 28$, how many money he had before? Please anwer with the pattern, thank you

Answers

(1-1/3)x*(1-1/5)=28 8/15x=28 x=52.5. Therefore, he had 52.5$before

What is the base 10 representation of 11102?

Answers

Answer:

Step-by-step explanation:

The base two number one one one zero is equal to one times eight, plus one times four, plus one times two, plus zero times one, which simplifies to fourteen.

Answer:

1.1102 * 10^4

Step-by-step explanation:

11102

= 1.1102 * 10^4

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