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oksano4ka [1.4K]

3 years ago

14

(1 point) For each of the indefinite integrals below, choose which of the following substitutions would be most helpful in evalu

ating the integral. Enter the appropriate letter (A,B, or C) in each blank. DO NOT EVALUATE THE INTEGRALS. A. x=6tanθ B. x=6sinθ C. x=6secθ

1 answer:

PIT_PIT [208]3 years ago

5 0

Answer:

1- optionC X= 6secθ

2- option B. X= 6sin(θ)

3- option A. X= 6tan(θ)

4- option C. X= 6sec(θ)

5- option A. X= 6tan(θ)

Step-by-step explanation:

Attached is the full question

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Step-by-step explanation:

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2 years ago

I need help with these. They are hard.<br><br>

iragen [17]

Answer:

Find the explicit from for the sequence $t_n=t_{n-1}+4,t=6$ :

$a_n=4n+2$

This next question I edited a bit. Your question just says find the four terms. I'm assuming they meant the first four. I also changed the c to an $a$ .

Find the first four terms of the sequence given by: $a_n=n a_{n-1}-3,a_1=2$ :

a) 2,1,0.-3

You might want to read that second question again because there is errors in the question or things that don't really make sense. I made my own interpretation of the problem based on my own mathematical experience.

Step-by-step explanation:

So your first question actually says that you can find a term by taking that term's previous term and adding 4.

So more terms of the sequence starting at first term 6 is:

6,10,14,18,....

This is an arithmetic sequence. When thinking of arithmetic sequences you should just really by thinking about equations of lines.

Let's say we have this table for (x,y):

x | y

----------

1 6

2 10

3 14

4 18

So we already know the slope which is the common difference of an arithmetic sequence.

We also know point slope form of a line is $y-y_1=m(x-x_1)$ where m is the slope and $(x_1,y_1)$ is a point on the line. You can use any point on the line. I'm going to use the first point (1,6) with my slope=4.

$y-6=4(x-1)$

$y=6+4(x-1)$ :I added 6 on both sides here.

$y=6+4x-4$ :I distribute here.

$y=4x+2$ :This is what I get after combining like terms.

So $a_n=y$ and $x=n$ so you have:

$a_n=4n+2$

---------------------------------------------------------------------------------------

The first four terms of this sequence will be given by:

$a_1,a_2,a_3,a_4$

$a_1=2$ so it is between choice a, c, and d.

$a_n=na_{n-1}-3$

To find $a_2$ replace n with 2:

$a_2=2a_{1}-3$

$a_2=2(2)-3$

$a_2=4-3$

$a_2=1$

So we have to go another further the only one that has first two terms 2,1 is choice a.

7 0

2 years ago