Lim[(sqrt(cos(2x))-cubicrootof(cos(x))]/arctg(x^2) when x->0

Answers

Answer 1

Answer: $\lim\limits_(x\to0)\frac{√(cos2x)-\sqrt[3]{cosx}}{arctanx^2}=\left[(0)/(0)\right]\n\nDe\ L'Hospital's\ rule:\n\n\lim\limits_(x\to0)\frac{√(cos2x)-\sqrt[3]{cosx}}{arctanx^2}=\lim\limits_(x\to0)\frac{(√(cos2x)-\sqrt[3]{cosx})'}{(arctanx^2)'}=(*)\n-------------------------------\n(√(cos2x)-\sqrt[3]{cosx})'=(-sin2x)/(√(cos2x))-\frac{-sinx}{3\sqrt[3]{cos^2x}}=\frac{-2sinxcosx\cdot3\sqrt[3]{cos^2x}+sinx√(cos2x)}{3√(cos2x)\cdot\sqrt[3]{cos^2x}}\n\n(arctanx^2)'=(2x)/(x^2+1)$

$-------------------------------\n(*)=\lim\limits_(x\to0)\frac{-6sinxcosx\sqrt[3]{cos^2x}+sinx√(cos2x)}{3\sqrt[3]{cos^2x}\cdot√(cos2x)}:(2x)/(x^4+1)\n\n=\lim\limits_(x\to0)\frac{-sinx(6cosx\sqrt[3]{cos^2x}-√(cos2x))}{3\sqrt[3]{cos^2x}\cdot√(cos2x)}\cdot(x^4+1)/(2x)\n\n=\lim\limits_(x\to0)(-sinx)/(x)\cdot\frac{(6cosx\sqrt[3]{cos^2x}-√(cos2x))(x^4+1)}{6}=-1\cdot\frac{(6\cdot1\sqrt[3]{1^2}-\sqrt1)(0+1)}{6}\n\n=-1\cdot(5)/(6)=-(5)/(6)$

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A school survey of 90 sixth graders showed that 25% of them play basketball and about 17% play soccer. What are the chances that a sixth grader plays basketball AND soccer?

Answers

Answer:

0.0425

Step-by-step explanation:

probability of basket player = 0.25

probability of being a soccer player = 0.17

chances that a sixth grader plays basketball AND soccer = 0.25×0.17 = 0.0425

I need help finding the radius to this question:Circle o is represented by the equation (x+2)^2 + (y-5)^2=48.The coordinates of the center and the length of the radius of circle O are....

Answers

I'm sorry I can't think of a way to explain this right now. Maybe my brain
is just fried from a long day, I don't know. I really hate it when people get
on here and hand out answers with no explanation, but that's the best that
I can do right now.

I can tell you that the center of the circle is the point (-2, 5),
and the length of the radius is √48 = 4√3 = about 6.928 .

To find the center you would set (x+2) and (y-5) equal to 0. Solving for x and y, you get that x=-2 and y=5. Center: (-2,5). You can also think of this as solving for the additive inverse of 2 and -5. To find the radius, simply take the square root of 48, leaving you with 4√3.
Remember the from is (x-h)²+(y-k)²=R² To find R just take the square root of the constant.

A graph is constructed such that time (in hours)is the x-variable and distance (in miles) is the y-variable. If you plot the distance that the car travels on the graph traveling at a speed 60 miles per hour, what is the slope of the graph?

Answers

For every one mile (across) the line will go up 60. This line (from (0,0) ) is therefore y = 60x
:D

1/3(9x-24) x simplify the expression

Answers

I hope this helps you

1/3 (9x-24)

1/3.9x-1/3.24

3x-8

A line has____rotational symmetry,

Answers

Answer:

two-fold

Step-by-step explanation:

you can rotate it one other way for it to look the exact same, meaning there are a total of 2 ways to rotate it

Answer:

A line has two-fold rotational symmetry; A

Step-by-step explanation:

One fold when it is turned 180°

And another fold when it is turned 360°

Hope that helps!!

The standard normal curve shown below models the population distribution of a random variable. What proportion of the values in the population does not lie between the two z-scores indicated on the diagram?z=-1.25
z=0.80

Answers

Answer:

0.3175

Step-by-step explanation:

z=-1.25 from table is .1056

z=.80 from table is .7881

subtract from each other =.6825

Subtract from the whole is 1-.6825=0.3175

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