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Mama L [17]
3 years ago
6

I need to find the limit

Mathematics
1 answer:
Digiron [165]3 years ago
8 0
For x=\dfrac{1}{2} the function is undefined.

\displaystyle
\lim_{x\to\tfrac{1}{2}^-} x\sec (\pi x)=\infty\\
\lim_{x\to\tfrac{1}{2}^+} x\sec (\pi x)=-\infty\\\\
\lim_{x\to\tfrac{1}{2}^-}x\sec (\pi x)\not = \lim_{x\to\tfrac{1}{2}^+}x\sec (\pi x)

So, the limit doesn't exist.
You might be interested in
What is the length of side AB of parallelogram ABCD?<br> units<br> 4g - 8<br> B<br> q+4
Andrews [41]

Answer:

8 units

Step-by-step explanation:

» <u>Concepts</u>

Parallelogram Side Theorem states that the opposite sides of a parallelogram are congruent, meaning they have the same length.

» <u>Application</u>

In this case, we're asked to apply the theorem to find the value of q and then find the length of AB. Thus, we have to set up the equation 4q - 8 = q + 4.

» <u>Solving</u>

Step 1: Subtract q from both sides.

  • 4q-8-q=q+4-q
  • 3q-8=4

Step 2: Add 8 to both sides.

  • 3q-8+8=4+8
  • 3q=12

Step 3: Divide both sides by 3.

  • 3q/3 = 12/3
  • q=4

Step 4: Plug in the value of q for side AB.

  • 4(4)-8
  • 16-8
  • 8

Therefore, the answer is 8 units.

6 0
2 years ago
Keith as 11/12 hours to play, he has already played 1/4. which is the best estimate of the fractional part of an hour he has lef
____ [38]

Answer:

The best estimate is greater than 1/2 but less than 3/4

Step-by-step explanation:

If you multiply 1/4 by 3/3 (which is also 1), you can change the denominator without changing the value.  So 1/4 is equal to 3/12.

Since keith has 11/12 hours to play, and he has already played 3/12 hours, subtract 3/12 from 11/12 to get 8/12 hours. This is how much time he has left to play.  

If you simplify 8/12 hours, you get 2/3 hours.

So the best estimate would be: greater than 1/2 but less than 3/4.

4 0
3 years ago
Triangle MNO is reflected over the x-axis and then translated up 4 and right 3. On a coordinate plane, triangle O M N has points
Schach [20]

Answer:

Option A. Translate the pre-image down 4 and right 3 and then reflect the figure over the x-axis

Step-by-step explanation:

8 0
3 years ago
I really think it’s B ...Help?
kvv77 [185]
The correct answer is c y-5=4(x-7)
7 0
3 years ago
In a particular faculty 60% of students are men and 40% are women. In a random sample of 50 students what is the probability tha
zimovet [89]

Answer:

a) The expected value is given by:

E(X) = np = 50*0.4 = 20

and the variance is given by:

Var(X) =np(1-p) = 50*0.4*(1-0.4) = 12

b) P(X>25)= 1-P(X\leq 25)

And we can find this probability with the following Excel code:

=1-BINOM.DIST(25,50,0.4,TRUE)

And we got:

P(X>25)= 1-P(X\leq 25)=0.0573

c) 1) Random sample (assumed)

2) np= 50*0.4= 20 >10

n(1-p) =50*0.6= 30>10

3) Independence (assumed)

Since the 3 conditions are satisfied we can use the normal approximation:

X \sim N(\mu = 20 , \sigma= 3.464)

d) P(X>25) = 1-P(Z< \frac{25-20}{3.464}) = 1-P(z

e) P(X>25)= P(X>25.5) = 1-P(X \leq 25.5)

P(X>25)= P(X>25.5) = 1-P(X \leq 25.5)= 1-P(Z

Step-by-step explanation:

Previous concepts

The binomial distribution is a "DISCRETE probability distribution that summarizes the probability that a value will take one of two independent values under a given set of parameters. The assumptions for the binomial distribution are that there is only one outcome for each trial, each trial has the same probability of success, and each trial is mutually exclusive, or independent of each other".

Let X the random variable of interest, on this case we now that:

X \sim Binom(n=50, p=0.4)

The probability mass function for the Binomial distribution is given as:

P(X)=(nCx)(p)^x (1-p)^{n-x}

Where (nCx) means combinatory and it's given by this formula:

nCx=\frac{n!}{(n-x)! x!}

Part a

The expected value is given by:

E(X) = np = 50*0.4 = 20

and the variance is given by:

Var(X) =np(1-p) = 50*0.4*(1-0.4) = 12

Part b

For this case we want to find this probability:

P(X>25)= 1-P(X\leq 25)

And we can find this probability with the following Excel code:

=1-BINOM.DIST(25,50,0.4,TRUE)

And we got:

P(X>25)= 1-P(X\leq 25)=0.0573

Part c

1) Random sample (assumed)

2) np= 50*0.4= 20 >10

n(1-p) =50*0.6= 30>10

3) Independence (assumed)

Since the 3 conditions are satisfied we can use the normal approximation:

X \sim N(\mu = 20 , \sigma= 3.464)

Part d

We want this probability:

P(X>25) = 1-P(Z< \frac{25-20}{3.464}) = 1-P(z

Part e

For this case we use the continuity correction and we have this:

P(X>25)= P(X>25.5) = 1-P(X \leq 25.5)

P(X>25)= P(X>25.5) = 1-P(X \leq 25.5)= 1-P(Z

4 0
3 years ago
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