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1 year ago

Determine a limit for a piecewise function

Mathematics

1 answer:

laila [671]1 year ago

8 0

The limit for the given piecewise function does not exist(DNE).

4th option is correct.

<h3 /><h3>What is the limit of a function?</h3>

In mathematics, limits are the points at which a function approaches the output for the specified input values. Calculus and mathematical analysis depend heavily on limits, which are required to determine integrals, derivatives, and continuity. It is applied during the analysis process and always focuses on the function's behavior at a certain time.

Unique real numbers are limits in mathematics.

According to the question,

Left hand limit of the function= -5(3)+4 = -15+4 = -11

Right hand limit of the function= (3)(3)+2 = 11

As the left and right-hand limits are not equal. Thus, the limit of the function does not exist.

Learn more about limits here:

brainly.com/question/23935467

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How do you find an average?

wlad13 [49]

Answer:

Finding the average is a very straightforward concept. If you have a set of numbers, the average is found by adding all numbers in the set and dividing their sum by the total number of numbers added in the set.

example;

16, 17, 5, 27, 30, 20, 4, 1, 19, 9

add all 10 of these numbers together

16 + 17+ 5+27+30+4+1+19+9 = 148

divide 128 by 10

148 / 10 = 14.8

14.8 is the average

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2 years ago

Hong is a software salesman. His base salary is $2500 , and he makes an additional $110 for every copy of Math is Fun he sells.

nalin [4]

Pn=? 2500 +110×22=4920

4 0

3 years ago

5/6+1/4= to write as a whole fraction

Maksim231197 [3]

Step-by-step explanation:

5/6+1/4

3/12+10/12=13/12=

well You need to find number which can divide into six and four and the smallest to make finding It easy. 12 is the smallest

7 0

2 years ago

Read 2 more answers

How many terms of the arithmetic sequence {1,22,43,64,85,…} will give a sum of 2332? Show all steps including the formulas used

MA_775_DIABLO [31]

There's a slight problem with your question, but we'll get to that...

Consecutive terms of the sequence are separated by a fixed difference of 21 (22 = 1 + 21, 43 = 22 + 21, 64 = 43 + 21, and so on), so the n-th term of the sequence, a (n), is given recursively by

• a (1) = 1

• a (n) = a (n - 1) + 21 … … … for n > 1

We can find the explicit rule for the sequence by iterative substitution:

a (2) = a (1) + 21

a (3) = a (2) + 21 = (a (1) + 21) + 21 = a (1) + 2×21

a (4) = a (3) + 21 = (a (1) + 2×21) + 21 = a (1) + 3×21

and so on, with the general pattern

a (n) = a (1) + 21 (n - 1) = 21n - 20

Now, we're told that the sum of some number N of terms in this sequence is 2332. In other words, the N-th partial sum of the sequence is

a (1) + a (2) + a (3) + … + a (N - 1) + a (N) = 2332

or more compactly,

$\displaystyle\sum_{n=1}^N a(n) = 2332$

It's important to note that N must be some positive integer.

Replace a (n) by the explicit rule:

$\displaystyle\sum_{n=1}^N (21n-20) = 2332$

Expand the sum on the left as

$\displaystyle 21 \sum_{n=1}^N n-20\sum_{n=1}^N1 = 2332$

and recall the formulas,

$\displaystyle\sum_{k=1}^n1=\underbrace{1+1+\cdots+1}_{n\text{ times}}=n$

$\displaystyle\sum_{k=1}^nk=1+2+3+\cdots+n=\frac{n(n+1)}2$

So the sum of the first N terms of a (n) is such that

21 × N (N + 1)/2 - 20N = 2332

Solve for N :

21 (N ² + N) - 40N = 4664

21 N ² - 19 N - 4664 = 0

Now for the problem I mentioned at the start: this polynomial has no rational roots, and instead

N = (19 ± √392,137)/42 ≈ -14.45 or 15.36

so there is no positive integer N for which the first N terms of the sum add up to 2332.

4 0

2 years ago

A: HL B: ASA C: SSS D: SAS

evablogger [386]

Answer:

D: SAS

Step-by-step explanation:

6 0

2 years ago