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Vikki [24]
2 years ago
5

Reallyyy need helpppppppppp

Mathematics
1 answer:
MAXImum [283]2 years ago
8 0

Answer:

r = 3

Step-by-step explanation:

Slope of a line passing through two points (x_1,y_1) and (x_2,y_2) is given by the formula,

Slope 'm' = \frac{y_2-y_1}{x_2-x_1}

Slope of a line passing through (4, 2) and (r, -6) is 8.

8 = \frac{2+6}{4-r}

8(4 - r) = 8

4 - r = 1

r = 4 - 1

r = 3

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Pls help this is pretty urgent
KIM [24]

Answer:

(a)  0

(b)  f(x) = g(x)

(c)  See below.

Step-by-step explanation:

Given rational function:

f(x)=\dfrac{x^2+2x+1}{x^2-1}

<u>Part (a)</u>

Factor the <u>numerator</u> and <u>denominator</u> of the given rational function:

\begin{aligned} \implies f(x) & = \dfrac{x^2+2x+1}{x^2-1} \\\\& = \dfrac{(x+1)^2}{(x+1)(x-1)}\\\\& = \dfrac{x+1}{x-1}\end{aligned}

Substitute x = -1 to find the limit:

\displaystyle \lim_{x \to -1}f(x)=\dfrac{-1+1}{-1-1}=\dfrac{0}{-2}=0

Therefore:

\displaystyle \lim_{x \to -1}f(x)=0

<u>Part (b)</u>

From part (a), we can see that the simplified function f(x) is the same as the given function g(x).  Therefore, f(x) = g(x).

<u>Part (c)</u>

As x = 1 is approached from the right side of 1, the numerator of the function is positive and approaches 2 whilst the denominator of the function is positive and gets smaller and smaller (approaching zero).  Therefore, the quotient approaches infinity.

\displaystyle \lim_{x \to 1^+} f(x)=\dfrac{\to 2^+}{\to 0^+}=\infty

5 0
1 year ago
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