A cereal box can hold 144 cubic inches of cereal. Suppose the box is 8 inches long and 1.5 inches wide. How tall is the box?

Explain why g(x)= {sin π/x if =0, 1 if x=0 , is not continuous a x=0

stepladder [879]

Answer:

$\lim_{x\rightarrow 0}g(x)$ does not exist.

D is correct.

Step-by-step explanation:

We are given,

$g(x)=\left\{\begin{matrix} \sin\left ( \dfrac{\pi}{x} \right )& \ \ \ if\ \ x\neq 0\\ 1& \ \ \ if\ \ x\neq 0\end{matrix}\right.$

For continuous function, LHL=RHL=f(0)

Using squeeze theorem,

If $g(x)\leq f(x)\leq h(x)$

then $\lim_{x\rightarrow a}g(x)\leq \lim_{x\rightarrow a}f(x)\leq \lim_{x\rightarrow a}h(x)$

As we know

$-1\leq \sin\left ( \dfrac{\pi}{x} \right )\leq 1$

Apply Limit both sides

$\lim_{x\rightarrow 0}(-1)\leq \lim_{x\rightarrow 0}\sin\left ( \dfrac{\pi}{x} \right )\leq \lim_{x\rightarrow a}1$

$\lim_{x\rightarrow 0}(-1)=-1$

$\lim_{x\rightarrow 0}(1)=1$

$-1\neq 1$

$LHL\neq RHL=g(0)$

If $LHL\neq RHL$ then limit does not exist.

Hence, $\lim_{x\rightarrow 0}g(x)$ does not exist.

D is correct.

7 0

3 years ago

How do i solve x-y+8 if x=5 and y=3?

Vitek1552 [10]

First, you input the numbers that have the variables. So the first equation would be 5-3+8. That equation equals 10.

7 0

3 years ago

Read 2 more answers

Pls help, don’t quite understand these at all and need the correct answers:)

Dima020 [189]

9514 1404 393

Answer:

cos(A) ≈ 0.9165

Step-by-step explanation:

Put the given value into the given relation and solve for the unknown.

sin²(A) +cos²(A) = 1

(2/5)² + cos²(A) = 1

cos²(A) = 1 -4/25 = 21/25 . . . . . subtract (2/5)²

cos(A) = √(21/25) ≈ 0.9165 . . . . . take the square root

_____

Both sine and cosine are positive in Quadrant I, so we're only interested in the positive square root.

8 0

3 years ago

A certain gas station requires a minimum of $5 to use a debit card. You plan on buying a soda and however many bags of cheetos r

vekshin1

Answer:

1.20 + 1.40x ≥ 5, or $1.20 + $1.40x ≥ $5

Step-by-step explanation:

So since you are only buying 1 soda and you are buying multiple bags of Cheetos so you are able to use you debit card and meet the requirement of at least $5, you can make the inequality:

1.20 + 1.40x ≥ 5, or $1.20 + $1.40x ≥ $5

where x is the number of bags of Cheetos.

6 0

3 years ago

Eighteen students are members of the Science Club. This is 1/3 the number of students in the three sections of

Usimov [2.4K]

Answer:

18

Step-by-step explanation:

1/3 = 18 we are givien the number of kids in one section so if each section will have an equal amount of kids each section will have 18 kids.

7 0

3 years ago