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STALIN [3.7K]
1 year ago
12

Find lim f(x) if f(x) x->5 = { -x² -1, x #5 -3, x=5

Mathematics
1 answer:
Alex73 [517]1 year ago
3 0

Given

f(x) = \begin{cases} -x^2 - 1 & \text{if }x \neq 5 \\ -3 & \text{if }x=5 \end{cases}

we have

\displaystyle \lim_{x\to5} f(x) = \lim_{x\to5} (-x^2-1) = -5^2-1 = \boxed{-26}

since we are <em>approaching</em> x=5, so effectively x\neq 5 and we use the definition of f(x) under that condition.

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The triangle below is isosceles. Find the length of side xx in simplest radical form with a rational denominator.
coldgirl [10]

Answer:

Solution given:

Since the given triangle is isosceles and right angled triangle

perpendicular [p]=base[b]=x

hypotenuse [h]=6

we have

by using Pythagoras law

p²+b²=h²

x²+x²=6²

2x²=36

x²=36/2

x²=18

x=\sqrt{18}

<u>x</u>=\bold{3\sqrt{2}}

6 0
3 years ago
The lines below are parallel. If the slope of the green line is -4, what is the slope of the red line? 5 m = O A. 4 B. -4 O c. 1
Kobotan [32]

Answer:

-4

Step-by-step explanation:

Parallel lines have the same slope

-4

6 0
2 years ago
Read 2 more answers
Write x^3-11x^2 in standard form
Vika [28.1K]

Answer:

The answer is x^3 - 11x^2

Step-by-step explanation:

Write in standard form.

Hoped this helped!

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8 0
2 years ago
Select the graph of the solution. Click until the correct graph appears.<br> x ≥ 4
Mkey [24]
I think the correct answer from the choices listed above would be the second graph. The given inequality is given as x is greater than or equal to 4. So, the graph should include the value 4 then to the right of 4 in the number line. Hope this answers the question.
7 0
3 years ago
Read 2 more answers
Use synthetic division and remainder theorem p(x) = 3x^3 - 5x^2 - x + 2. p(-1/3)=
Alik [6]

Answer:

5/3

Step-by-step explanation:

-1/3 goes on the outside and since we have our polynomial in standard form with no in between terms missing, 3,-5,-1,2 go inside because they are the coefficients of our polynomial.

-1/3   |   3      -5          -1          2

       |

         -------------------------------------

First step bring the 3 down inside. (3+0=3)

-1/3   |   3      -5          -1          2

       |

         -------------------------------------

           3

Whatever goes below the bar, must be multiplied by outside number and put directly below next number inside.

-1/3   |   3      -5          -1          2

       |             -1

         -------------------------------------

           3

The numbers lined up vertically are added to get the numbers underneath the bar.

-1/3   |   3      -5          -1          2

       |             -1

         -------------------------------------

           3        -6

Again any number below the bar gets multiply to the number outside.

-1/3   |   3      -5          -1          2

       |             -1          2

         -------------------------------------

           3        -6

Again the numbers lined up vertically above the bar get added to get the number that goes underneath the bar there.

-1/3   |   3      -5          -1          2

       |             -1          2

         -------------------------------------

           3        -6          1

Multiply to outside number 1(-1/3)=-1/3.

This goes under the 2 inside.

-1/3   |   3      -5          -1          2

       |             -1          2          -1/3

         -------------------------------------

           3        -6          1

The last number we are fixing to be put is the remainder of (3x^3-5x^2-x+2)/(x+1/3) or you could say it is the value of p(-1/3) since:

P(x)/(x-c)=Q(x)+R/(x-c)

Multiply both sides by (x-c):

P(x)=Q(x)(x-c)+R

If you evaluate P at x=c, we get R:

P(c)=Q(c)(c-c)+R

P(c)=Q(c)*0+R

P(c)=R.

Let's finish:

-1/3   |   3      -5          -1          2

       |             -1          2          -1/3

         -------------------------------------

           3        -6          1         5/3

This means p(-1/3)=5/3.

We could have also got this by directly plugging in (-1/3) for x into 3x^3-5x^2-x+2.

7 0
3 years ago
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