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jenyasd209 [6]
3 years ago
13

Calculus1 help involving graphs.

Mathematics
1 answer:
tatuchka [14]3 years ago
4 0

Answer:

-0.67

Step-by-step explanation:

Pick two points on the tangent line, and find the slope between them.

The line passes through approximately (30,145) and (90, 105).

m = (105 − 145) / (90 − 30)

m = -0.67

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salantis [7]

Answer:

\displaystyle  \lim_{x \to 0} \frac{\sqrt{cos(2x)} - \sqrt[3]{cos(3x)}}{sin(x^2)} = \frac{1}{2}

General Formulas and Concepts:

<u>Calculus</u>

Limits

Limit Rule [Variable Direct Substitution]:                                                                     \displaystyle \lim_{x \to c} x = c

L'Hopital's Rule

Differentiation

  • Derivatives
  • Derivative Notation

Basic Power Rule:

  1. f(x) = cxⁿ
  2. f’(x) = c·nxⁿ⁻¹

Derivative Rule [Chain Rule]:                                                                                    \displaystyle \frac{d}{dx}[f(g(x))] =f'(g(x)) \cdot g'(x)

Step-by-step explanation:

We are given the limit:

\displaystyle  \lim_{x \to 0} \frac{\sqrt{cos(2x)} - \sqrt[3]{cos(3x)}}{sin(x^2)}

When we directly plug in <em>x</em> = 0, we see that we would have an indeterminate form:

\displaystyle  \lim_{x \to 0} \frac{\sqrt{cos(2x)} - \sqrt[3]{cos(3x)}}{sin(x^2)} = \frac{0}{0}

This tells us we need to use L'Hoptial's Rule. Let's differentiate the limit:

\displaystyle  \lim_{x \to 0} \frac{\sqrt{cos(2x)} - \sqrt[3]{cos(3x)}}{sin(x^2)} = \displaystyle  \lim_{x \to 0} \frac{\frac{-sin(2x)}{\sqrt{cos(2x)}} + \frac{sin(3x)}{[cos(3x)]^{\frac{2}{3}}}}{2xcos(x^2)}

Plugging in <em>x</em> = 0 again, we would get:

\displaystyle \lim_{x \to 0} \frac{\frac{-sin(2x)}{\sqrt{cos(2x)}} + \frac{sin(3x)}{[cos(3x)]^{\frac{2}{3}}}}{2xcos(x^2)} = \frac{0}{0}

Since we reached another indeterminate form, let's apply L'Hoptial's Rule again:

\displaystyle \lim_{x \to 0} \frac{\frac{-sin(2x)}{\sqrt{cos(2x)}} + \frac{sin(3x)}{[cos(3x)]^{\frac{2}{3}}}}{2xcos(x^2)} = \lim_{x \to 0} \frac{\frac{-[cos^2(2x) + 1]}{[cos(2x)]^{\frac{2}{3}}} + \frac{cos^2(3x) + 2}{[cos(3x)]^{\frac{5}{3}}}}{2cos(x^2) - 4x^2sin(x^2)}

Substitute in <em>x</em> = 0 once more:

\displaystyle \lim_{x \to 0} \frac{\frac{-[cos^2(2x) + 1]}{[cos(2x)]^{\frac{2}{3}}} + \frac{cos^2(3x) + 2}{[cos(3x)]^{\frac{5}{3}}}}{2cos(x^2) - 4x^2sin(x^2)} = \frac{1}{2}

And we have our final answer.

Topic: AP Calculus AB/BC (Calculus I/I + II)

Unit: Limits

6 0
3 years ago
Geometry help!!
Eduardwww [97]
It would be A, Side Angle Side (SAS).  Because you are given we congruent sides, and tow right angles.  Using the reasoning of "If two two angles are both right angles then they are congruent" you can prove the angles congruent. 

The reason it is not HL is because HL is used when it is given a right angle and the hypotenuse and one of the legs congruent.  Therefore the only choice is Side Angle Side (SAS).
3 0
3 years ago
A sports club needs to raise at least $500 by selling chocolate bars for $2.50 each. Sebastian wants to know how many chocolate
mario62 [17]

Answer:

The inequality should be written as $2.50 times c is greater than or equal to c.

Step-by-step explanation:

First, identify what you know:

1) Each chocolate bar is $2.50

2) Sebastian needs to raise at least $500

So, Sebastian needs to sell at least enough chocolate bars to hit $500. The inequality cannot be written as less than or equal to, because he can't sell less than the number of chocolate bars needed to make $500.

Automatically, I can calculate the minimum number of bars he'll need to sell.

500/2.50 = 200 chocolate bars minimum

c must equal greater than or equal to $500, for Sebastian to raise enough money! So, basically Sebastian has to sell 200 bars OR more.

Hope this helps! :)

4 0
3 years ago
Read 2 more answers
In the diagram, PQRS TUVW$ . Find the value of x
Feliz [49]

Answer:

The answer is x = 8.

Step-by-step explanation:

6 0
3 years ago
A spherical ball has a radius of 12 cm. The cost to cover the sphere is $0.05/cm^2. The total cost to cover the ball is:
Umnica [9.8K]

Answer:

Step-by-step explanation:

surface area of sphere=4πr²=4π×12²=576π

≈576×3.1416

≈1809.5616 cm²

cost to cover=1809.5616×0.05=$90.47808≈$90.48

7 0
2 years ago
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