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olga55 [171]
3 years ago
13

Find the limit !!!!!!

Mathematics
1 answer:
Tasya [4]3 years ago
6 0

Answer:

1/8.

Step-by-step explanation:

Use l'Hopitals rule - we find the derivative of top and bottom of the fraction.

Derivative of the numerator = 0 - 1/2 (16 - x)^-1/2  -1

=  1 / [ 2 * (16 - x)^1/2

Derivative of the denominator =  1

When x approaches 0 this is 1 / (2*4)

= 1/8.

Another way to do this is to multiply top and bottom by  4 + (16 - x)^1/2

This  becomes   16 - (16 - x) / x(4 + (16-x)^1/2)

= 1 / (4 + (16 + x)^1/2

When x ---> 0

this = 1 /(4 + 4)

= 1/8.

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For the following exercises, find (f ∘ g)(x) and (g ∘ f)(x) for each pair of functions.
Rufina [12.5K]

Answer:

The value of $(f \circ g)(x)$ is 17-18x and $(g \circ f)(x)$ is -7-18x.

Step-by-step explanation:

It is given in the question functions f(x) as 3x+2 and g(x)=5-6x.

It is required to find $(f \circ g)(x)$ and $(g \circ f)(x)$.

To find $(f \circ g)(x)$, substitute g(x) for x in f(x) and simplify the expression.

To find $(g \circ f)(x)$, substitute f(x) for x in g(x) and simplify the expression.

Step 1 of 2

Substitute g(x) for x in f(x) and simplify the expression.

$$\begin{aligned}&(f \circ g)(x)=f(5-6 x) \\&(f \circ g)(x)=3(5-6 x)+2 \\&(f \circ g)(x)=15-18 x+2 \\&(f \circ g)(x)=17-18 x\end{aligned}$$

Step 2 of 2

Substitute f(x) for x in g(x) and simplify the expression.

$$\begin{aligned}&(g \circ f)(x)=g(3 x+2) \\&(g \circ f)(x)=5-6(3 x+2) \\&(g \circ f)(x)=5-18 x-12 \\&(g \circ f)(x)=-7-18 x\end{aligned}$$

5 0
2 years ago
Solve each triangle - find any missing side and angle measures. Round answers to the nearest tenth.
Basile [38]

The sides of the right-angle triangle will be 16 units and 20.30 units. And the missing angle will be 52°.

<h3>What is a right-angle triangle?</h3>

It's a form of a triangle with one 90-degree angle that follows Pythagoras' theorem and can be solved using the trigonometry function.

The side AC will be

tan 38° = 12.5 / AC

      AC = 15.999

      AC ≈ 16 units

Then the side AB will be

AB² = 12.5² + 16²

 AB = 20.30 units

We know that the angle sum is 180 degrees. Then we have

∠A + ∠B + ∠C = 180°

38° + ∠B + 90° = 180°

                  ∠B = 52°

More about the right-angle triangle link is given below.

brainly.com/question/3770177

#SPJ1

6 0
2 years ago
What is the next number in the sequence 3, 12, 24, 33, 66
ExtremeBDS [4]
75.
Explanation: from 3 to 12, you add 9, and then double the 12 to get to 24, and then add 9 again to get to 33, and double it to get 66, so the pattern is to add 9 and then double.
4 0
4 years ago
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Which ordered pair is a solution of the equation?
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6 0
3 years ago
Which solid has a greater volume?
Lady_Fox [76]

Answer:

C

Step-by-step explanation:

The volume of a cone is given by  V=\frac{1}{3}\pi r^2h

The volume of a cylinder is given by  V=\pi r^2 h

<em>Where h is the height and r is the radius</em>

The first figure is a cone with height 6 and radius 5, we can put it into the formula and find the volume:

\frac{1}{3}\pi r^2 h\\\frac{1}{3}\pi (5)^2 (6)\\=157.08

The second figure is a cylinder with height 50 and radius 1, we can put it into the formula and find the volume:

\pi r^2 h\\\pi (1)^2 (50)\\=157.08

We can see that they are equal. So answer choice C is right.

5 0
4 years ago
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