5.2 in expanded form

sergejj [24]

Answer:

A

Step-by-step explanation:

We are given the function:

$\displaystyle f(x) = \left\{ \begin{array}{ll} 2\cos(\pi x) \text{ for } x \leq -1 \\ \\ \displaystyle \frac{2}{\cos(\pi x)}\text{ for } x > -1 \end{array} \right.$

And we want to find:

$\displaystyle \lim_{x\to -1}f(x)$

So, we need to determine whether or not the limit exists. In other words, we will find the two one-sided limits.

Left-Hand Limit:

$\displaystyle \lim_{x\to-1^-}f(x)$

Since we are approaching from the left, we will use the first equation:

$\displaystyle =\lim_{x\to -1^-}2\cos(\pi x)$

By direct substitution:

$=2\cos(\pi (-1))=2\cos(-\pi)=2(-1)=-2$

Right-Hand Limit:

$\displaystyle \lim_{x\to -1^+}f(x)$

Since we are approaching from the right, we will use the second equation:

$=\displaystyle \lim_{x\to -1^+}\frac{2}{\cos(\pi x)}$

Direct substitution:

$\displaystyle =\frac{2}{\cos(\pi (-1))}=\frac{2}{\cos(-\pi)}=\frac{2}{(-1)}=-2$

So, we can see that:

$\displaystyle \displaystyle \lim_{x\to-1^-}f(x)=\displaystyle \lim_{x\to -1^+}f(x) =-2$

Since both the left- and right-hand limits exist and equal the same thing, we can conclude that:

$\displaystyle \lim_{x \to -1}f(x)=-2$

Our answer is A.

8 0

3 years ago

A store has 40 bags of potato

mixas84 [53]

Answer:

The percentage of the bags of the potato chips that are not cheddar-flavored is 25%. This is because there are 10 bags that are not cheddar-flavored and this divided by 40 bags, which is the total bags of the potato chips multiply by 100% gives 25%

Step-by-step explanation:

If there are 40 bags of potato chips and 30 are cheddar flavored, Then

40 - 30 = 10 bags are not cheddar flavored

Since the total bags is 40,

percentage potato chips that are not cheddar-flavored = 10/40 × 100%

= 25%

6 0

4 years ago

Which coordinate grid shows the correct locations of P(2, 1.5), point Q, which is a reflection of point P across the y-axis, and

svetlana [45]

It is not B and D, because R is not in the right place.

It is also not C, since P is not in the upper right quadrant, but the lower left one. The correct grid is A

3 0

3 years ago

X+2x^1/2 -63 solve for x

AysviL [449]

You factor this out. So x+2x^(1/2)-63. Factors into (x^(1/2)+9)(x^(1/2)-7). If you distribute it, you can see it gives you your original equation

6 0

3 years ago

What is the slope of the line which passes through the two given points? (Write the answer as a reduced fraction)

Sophie [7]

Answer:

slope = 0

Step-by-step explanation:

8 0

3 years ago

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