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butalik [34]
3 years ago
8

Use the given conditions to write an equation for the line in point-slope form and in slope-intercept form.

Mathematics
1 answer:
dem82 [27]3 years ago
8 0

Answer:

see explanation

Step-by-step explanation:

The equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

y = - 4x + 3 ← is in slope- intercept form

with slope m = - 4

• Parallel lines have equal slopes, thus

y = - 4x + c ← is the partial equation

To find c substitute (- 9, - 4) into the partial equation

- 4 = 36 + c ⇒ c = - 4 - 36 = - 40

y = - 4x - 40 ← in slope- intercept form

The equation of a line in point- slope form is

y - b = m(x - a)

where m is the slope and (a, b) a point on the line

here m = - 4 and (a, b) = (- 9, - 4), thus

y - (- 4) = - 4(x - (- 9)), that is

y + 4 = - 4(x + 9) ← in point- slope form

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Find the limit. Use l'Hospital's Rule if appropriate. If there is a more elementary method, consider using it. lim x→1 3x x − 1
Reika [66]

Answer:

<h2>3/2</h2>

Step-by-step explanation:

Given the limit of a function expressed as \lim_{x \to 1} (\dfrac{3x}{x-1} - \dfrac{3}{lnx}), we are to evaluate it. To evaluate it, we will simply substitute x = 1 into the function since the variable x tends to 1.

\lim_{x \to 1} (\dfrac{3x}{x-1} - \dfrac{3}{lnx})\\\\= (\dfrac{3(1)}{1-1} - \dfrac{3}{ln1})\\\\= \dfrac{3}{0} - \dfrac{3}{0}\\\\= \infty - \infty (ind)

Since we got an indeterminate function, we will find the LCM of the function and solve again.

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Applying L'hospital rule;

\frac{x}{y} = \lim_{x \to 1} \dfrac{d/dx(3xlnx-3(x-1))}{d/dx((x-1)lnx)}\\\\=  \lim_{x \to 1} \dfrac{3x(\frac{1}{x})+ 3lnx-3)}{(x-1)\frac{1}{x} +lnx}\\\\= \lim_{x \to 1} \dfrac{3 + 3lnx-3}{(x-1)\frac{1}{x} +lnx}\\\\= \frac{3ln1}{(1-1)\frac{1}{1} +ln1}\\\\= \frac{0}{0} (ind)

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<em>Hence the limit of the function is 3/2.</em>

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