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Ymorist [56]
2 years ago
6

Lim x →1+. 1- x/x² - 1

Mathematics
1 answer:
mamaluj [8]2 years ago
8 0

Answer:  \displaystyle \boldsymbol{-\frac{1}{2}}

================================================

Work Shown:

\displaystyle L = \lim_{\text{x}\to 1^{+}} \frac{1-\text{x}}{\text{x}^2-1}\\\\\\\displaystyle L = \lim_{\text{x}\to 1^{+}} \frac{-(\text{x}-1)}{(\text{x}-1)(\text{x}+1)}\\\\\\\displaystyle L = \lim_{\text{x}\to 1^{+}} \frac{-1}{\text{x}+1}\\\\\\\displaystyle L = \frac{-1}{1+1}\\\\\\\displaystyle L = -\frac{1}{2}\\\\\\

In the second step, I used the difference of squares rule to factor.

The (x-1) terms cancel which allows us to plug in x = 1. We plug this value in because x is approaching 1 from the right side.

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8 0
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Una llave llena un tanque en 4 horas y el desagüe lo vacía en 6 horas. ¿En cuánto tiempo se llenará el tanque, si ambas llaves s
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7 0
3 years ago
Determine if the system of equations has one solution, no solution or infinitely many solutions.
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x

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0

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−

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(

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−

3

x

)

+

(

4

y

−

16

y

)

=

(

−

8

−

(

−

32

)

)

(

0

)

+

(

−

12

y

)

=

(

−

8

+

32

)

−

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y

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24

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−

2

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x

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3

x

+

4

y

=

−

8

3

x

+

4

(

−

2

)

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−

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3

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−

8

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6 0
3 years ago
Let f(x)=x²+kx+4 and g(x)=x³+x²+kx+2k, where k is a real constant.
antoniya [11.8K]

The value of k such that the graph of f and the graph of g only intersect one is equal to 2.

The value of k such that the graph of f and the graph of g only intersect one is equal to 2. According to the image attached below, functions f(x) and g(x) intersect at point (x, y) = (0, 4) for k = 2.

<h3>How to find the value of the constant k of a system of two polynomic equations</h3>

Herein we have a system formed by two <em>nonlinear</em> equations, a <em>quadratic</em> equation and a <em>cubic</em> equation. Given the constraint that both function must only intersect once, we have the following expression:

f(x) - x² - k · x = 4       (1)

g(x) - x² - k · x = x³ + 2 · k        (2)

x³ + 2 · k = 4

x³ + 2 · (k - 2) = 0

If f and g must intersect once, then the roots must of the form:

(x - r)³ = x³ + 2 · (k - 2)

x³ - 3 · r · x² + 3 · r² · x - r³ = x³ + 2 · (k - 2)

Then, the following conditions must be met: - 3 · r · x² = 0, 3 · r² · x = 0. If x may be any real number, then r must be zero and the value of k must be:

2 · (k - 2) = 0

k - 2 = 0

k = 2

Therefore, the value of k such that the graph of f and the graph of g only intersect one is equal to 2. According to the image attached below, functions f(x) and g(x) intersect at point (x, y) = (0, 4) for k = 2.

To learn more on polynomic functions: brainly.com/question/24252137

#SPJ1

7 0
1 year ago
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