[MOVED] How to solve this??

[vileplayer]

Hello, guys! Please help me out, i am about to fail my midterm, now need to be prepared for that. How can i solve these problems??

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Spring Term Quiz of Calculus

1. \(\displaystyle \displaystyle{ \sum_{n=1}^{\infty}\,}\) \(\displaystyle \dfrac{3}{n}\, \) is convergent or divergent? Why? Explain by one of the known tests.

2. Find the area bounded by y = x² + 2x and y = x + 6.

3. Find the volume of the solid formed by the area bounded by y = x³, x = 1, and x = 3, and rotating by x-axis.

4. Find the sum of multiples of 3 between 111 and 1,111.

5. \(\displaystyle \displaystyle{\lim_{n\, \rightarrow \, \infty}\,}\) \(\displaystyle \left(\sqrt{\left(1\, -\, \dfrac{1}{n\, +\, 1}\right)^{n-1}\,}\right)\, =\, ?\)

6. If a₁₁ = 21 and a₂₂ = 23 find S₂₀.

7. If -8 is the first term of a geometric sequence and b₄ = -512, then find S₅.

8. \(\displaystyle \displaystyle{\sum_{n=1}^{\infty}}\,\) \(\displaystyle \dfrac{1}{5^{n-1}}\, =\, ?\)

 

[stapel]

i am about to fail my midterm, now need to be prepared for that. How can i solve these problems??

If you have no idea even how to get started on any of these exercises, then you need much more help than we can here provide. Perhaps you are exaggerating a bit? In hopes of the latter:

1. \(\displaystyle \displaystyle{ \sum_{n=1}^{\infty}\,}\) \(\displaystyle \dfrac{3}{n}\, \) is convergent or divergent? Why? Explain by one of the known tests.

What are the tests you've been given? How far have you gotten in applying them?

2. Find the area bounded by y = x² + 2x and y = x + 6.

What did you get as intersection points when you graphed these two lines? These points will be the endpoints of the integration interval. By nature of what you learned back in algebra, you knew, even before you graphed, that the quadratic would be below the straight line within that interval, making obvious which function will be subtracted from the other inside the integral. What did you get as your integral? Where are you stuck in the process of applying the Power Rule to the various terms of the integrand?

3. Find the volume of the solid formed by the area bounded by y = x³, x = 1, and x = 3, and rotating by x-axis.

Where are you stuck in the process?

4. Find the sum of multiples of 3 between 111 and 1,111.

Since 1 + 1 + 1 = 3, then 111 is a multiple of 3; specifically, 3*37 = 111. And 1,111/3 = 370.3333..., so 370*3 = 1,110 is the last of the multiples of 3 on the interval. So you're looking at 3*37 + ... + 3*370 = 3*(37 + ... + 370). Can you think of a way to convert this into a fairly straightforward summation formulation?

5. \(\displaystyle \displaystyle{\lim_{n\, \rightarrow \, \infty}\,}\) \(\displaystyle \left(\sqrt{\left(1\, -\, \dfrac{1}{n\, +\, 1}\right)^{n-1}\,}\right)\, =\, ?\)

What are your thoughts (in particular, about the natural exponential e)? What have you tried? You converted the two terms inside the radical to a common denominator, simplified, and... then what?

6. If a₁₁ = 21 and a₂₂ = 23 find S₂₀.

What are your thoughts? What have you tried?

7. If -8 is the first term of a geometric sequence and b₄ = -512, then find S₅.

The fourth term is the result of multiplying the first term by the common ratio three times. That is, b₄ = -8r³ = -512. Where did this lead you?

8. \(\displaystyle \displaystyle{\sum_{n=1}^{\infty}}\,\) \(\displaystyle \dfrac{1}{5^{n-1}}\, =\, ?\)

This is a fairly simple limit; you did similar computations with horizontal asymptotes back in algebra. Which test did you try here? What did you get?

Please be complete. Thank you!

 

[vileplayer]

plz. help me out. im stacked, tmrw is exam)

 

[stapel]

plz. help me out. im stacked, tmrw is exam)

Since the hints, helps, and suggestions have left you still unable even to begin any of the exercises, apparently you hadn't been exaggerating about not knowing any of this material. Unfortunately, there is no way, in a simple forum posting, to teach you the weeks or months of material necessary for this question set. Sorry.

Since you're not even able to get started on the algebra stuff, it seems that you probably need to drop back and start over in algebra or maybe pre-algebra. Somehow, you've been mis-placed into calculus. Perhaps an urgent meeting with your academic advisor would be a good idea...? If it is not possible to drop back, then your best bet would probably be to hire a qualified local tutor, setting aside an hour or two a day for concentrated face-to-face instruction. With hard work and a little luck, you may be able to catch up with the material in only a few months.

Good luck!