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Ad libitum [116K]
2 years ago
6

Show that f(x) = 2000x^4 and g(x) = 200x^4 grow at the same rate.

Advanced Placement (AP)
1 answer:
MAXImum [283]2 years ago
7 0

Answer:

The answer is "f(x) \ and \ g(x)\text {are in same rate }".

Explanation:

\to f(x) = 2000x^4\\\\ \to g(x) = 200x^4\\\\

\to \lim_{n \to \infty} \frac{f(x)}{g(x)}=\frac{2000x^4 }{200x^4}=\frac{2000}{200}=10\\\\\to  \lim_{n \to \infty} \frac{f(x)}{g(x)}= m\neq 10

So,f(x) \ and \ g(x) are in the same rate because M=10 is finite.

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The graph of x^2=-2+y+5cosy is shown for y=11
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(a)

We have been given an equation x^{2}=-2+y+5cosy. Upon taking derivative of this equation with respect to x on both the sides, we get:

2x=0+\frac{dy}{dx}+5(-siny)\frac{dy}{dx}\\2x=(1-5siny)\frac{dy}{dx}\Rightarrow \frac{dy}{dx}=\frac{2x}{1-5siny}

(b)

In order to write the equation of tangent line, we need to find the slope of the line. We know that point (3,11) lies on the graph. Therefore, we write the slope of the tangent as:

\text{Slope}=\frac{dy}{dx}=\frac{2(3)}{1-5sin(11)}=1

Therefore, equation of tangent line is:

y-y_{1}=m(x-x_{1})\Rightarrow y-11=1(x-3)\\y-11=x-3\\y=x+8

(c)

We know that slope of tangent is given as \frac{dy}{dx}=\frac{2x}{1-5siny}. The tangent will be vertical when denominator of slope is zero, that is:

1-5siny=0\Rightarrow siny=\frac{1}{5}\Rightarrow y=arcsin(\frac{1}{5})\\y=1.732,1.525, 3.063 \text{ etc.}

5 0
3 years ago
True or false- Gneiss is formed. The mineral grains in granite are flattened under pressure.
Vladimir79 [104]

Answer:

The correct answer is True

5 0
3 years ago
Which is the BEST example of showing agency in one’s education? A. making friends while getting your education B. taking the req
riadik2000 [5.3K]

The best example of showing agency in one’s education is: C. actively looking for new opportunities to build skills.

<h3>What is an agency?</h3>

An agency can be defined as the ability of an individual to identify valued goals, priorities and desired outcomes, so as to enhance the purposeful pursuit of those goals and desired outcomes proactively, efficiently and effectively.

In this context, we can infer and logically conclude that actively looking for new opportunities to build skills is the best example of showing agency in one’s education.

Read more on skills here: brainly.com/question/5064037

#SPJ1

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2 years ago
WILL GIVE BRAINLIEST!
Harman [31]

Answer:

reduce the cost of using fossil fuels

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3 years ago
Read 2 more answers
The regions bounded by the graphs of y=x2 and y=sin2x are shaded in the figure above. What is the sum of the areas of the shaded
Alex Ar [27]

Answer:

The sum of the area of the shaded regions = 0.248685

Explanation:

The sum of the area of the shaded region is given as follows;

The point of intersection of the graphs are;

y = x/2

y = sin²x

∴ At the intersection, x/2 = sin²x

sinx = √(x/2)

Using Microsoft Excel, or Wolfram Alpha, we have that the possible solutions to the above equation are;

x = 0, x ≈ 0.55 or x ≈ 1.85

The area under the line y = x/2, between the points x = 0 and x ≈ 0.55, A₁, is given as follows

1/2 × (0.55)×0.55/2 ≈ 0.075625

The area under the line y = sin²x, between the points x = 0 and x ≈ 0.55, A₂, is given using as follows;

\int\limits {sin^n(x)} \, dx = -\dfrac{1}{n} sin^{n-1}(x) \cdot cos(x) + \dfrac{n-1}{n} \int\limits {sin^{n-2}(x)} \, dx

Therefore;

A_2 = \int\limits^{0.55}_0 {sin^2x} \, dx = \dfrac{1}{2} \left [x -sin(x) \cdot cos(x) \right]_0 ^{0.55}

∴ A₂ =1/2 × ((0.55 - sin(0.55)×cos(0.55)) - (0 - sin(0)×cos(0)) ≈ 0.0522

The shaded area, A_{1 shaded} = A₁ - A₂ = 0.075625 - 0.0522 ≈ 0.023425

Similarly, we have, between points 0.55 and 1.85

A₃ = 1/2 × (1.85 - 0.55) × 1/2 × (1.85 - 0.55) + (1.85 - 0.55) × 0.55/2 = 0.78

For y = sin²x, we have;

A_4 = \int\limits^{1.85}_{0.55} {sin^2x} \, dx = \dfrac{1}{2} \left [x -sin(x) \cdot cos(x) \right]_{0.55} ^{1.85} \approx 1.00526

The shaded area, A_{2 shaded} = A₄ - A₃ = 1.00526 - 0.78 ≈ 0.22526

The sum of the area of the shaded regions, ∑A = A_{1 shaded} + A_{2 shaded}

∴ A = 0.023425 + 0.22526 = 0.248685

The sum of the area of the shaded regions, ∑A = 0.248685

8 0
3 years ago
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