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3 years ago

Does anyone know how to solve this? It’s really starting to stress me out.

Mathematics

1 answer:

bekas [8.4K]3 years ago

3 0

Answer:

π − 12

Step-by-step explanation:

lim(x→2) (sin(πx) + 8 − x³) / (x − 2)

If we substitute x = u + 2:

lim(u→0) (sin(π(u + 2)) + 8 − (u + 2)³) / ((u + 2) − 2)

lim(u→0) (sin(πu + 2π) + 8 − (u + 2)³) / u

Distribute the cube:

lim(u→0) (sin(πu + 2π) + 8 − (u³ + 6u² + 12u + 8)) / u

lim(u→0) (sin(πu + 2π) + 8 − u³ − 6u² − 12u − 8) / u

lim(u→0) (sin(πu + 2π) − u³ − 6u² − 12u) / u

Using angle sum formula:

lim(u→0) (sin(πu) cos(2π) + sin(2π) cos(πu) − u³ − 6u² − 12u) / u

lim(u→0) (sin(πu) − u³ − 6u² − 12u) / u

Divide:

lim(u→0) [ (sin(πu) / u) − u² − 6u − 12 ]

lim(u→0) (sin(πu) / u) + lim(u→0) (-u² − 6u − 12)

lim(u→0) (sin(πu) / u) − 12

Multiply and divide by π.

lim(u→0) (π sin(πu) / (πu)) − 12

π lim(u→0) (sin(πu) / (πu)) − 12

Use special identity, lim(x→0) ((sin x) / x ) = 1.

π (1) − 12

π − 12

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Order the numbers below least to greatest Please help me

n200080 [17]

The given numbers ordered from least to greatest is:

{√7 , 2.8..., π, √17, 4.6}

<h3>How to order the numbers from least to greatest?</h3>

First, we need to write all the given numbers in decimal form so we can accurately compare them.

The numbers are:

{4.6, √7, π, 2.8..., √17}

Rewriting all of these in decimal form:

√7 = 2.64

π = 3.14159265....

√17 = 4.12

Then the numbers are:

{4.6, 2.64, 3.14159265...., 2.8..., 4.12}

Now is easier to order these numbers, ordering them from least to greatest we will get:

{2.64, 2.8..., 3.14159265...., 4.12, 4.6}

Now, using the original notation we get:

{√7 , 2.8..., π, √17, 4.6}

If you want to learn more about ordering numbers:

brainly.com/question/1094377

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1 year ago

In the diagram m angle ACB = 61 Find m angle BCD

Marina86 [1]

we are given that

angle(ACF)=90

angle(ACB)=61

sum of all angles along any line is 180

so, we get

angle(ACF)+angle(ACD)=180

we can plug value

90+angle(ACD)=180

angle(ACD)=90

now, we can use formula

angle(ACD)=angle(ACB)+angle(BCD)

now, we can plug values

and we get

90=61+angle(BCD)

90-61=61-61+angle(BCD)

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3 years ago

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Which expression is equivalent to -3(4x-0.50)? PLEASEEEEEEEEEEEEE HELPPP

Misha Larkins [42]

Final Answer: $-12x + 1.5$

Steps/Reasons/Explanation:

Question: Which expression is equivalent to $-3(4x - 0.50)?$

Step 1: Expand by distributing terms.

$-3$ × $4x - 3$ × $-0.50$

Step 2: Simplify $-3$ × $4x$ to $-12x$ .

$-12x - 3$ × $-0.50$

Step 3: Simplify $3$ × $-0.50$ to $-1.5$ .

$-12x - (-1.5)$

Step 4: Remove parentheses and add.

$-12x + 1.5$

~I hope I helped you :)~

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3 years ago

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b means the y-intersept.

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Program for graph: Desmos

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