# calculus - power series ASAP please :)

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### calculus - power series ASAP please :)

using power series, integrate & evaluate to 4 dec. places integral from 0 to 1: sin x^2 dx i'm REALLY stuck on this. and i need help asap.. what is the inverse of "sin x^2" so that i could have it in a fraction that will fit the power series equation? and that is: (A)/(1-R) ...

### Calculus

Find a power series, centered @ x=0, for function f(x)=x/(1+2x). I know this is a maclaurin series, but my work doesn't get the right answer. Can you please show steps? Also,do all power series start with a 1, as in (1+2x+4x^2+...)? Thanks in advance!

### Calculus

Find a power series, centered @ x=0, for function f(x)=x/(1+2x). I know this is a maclaurin series, but my work doesn't get the right answer. Can you please show steps? Also,do all power series start with a 1, as in (1+2x+4x^2+...)? Thanks in advance!

### calculus

state the power series of an appropriate familiar function and use it to calculate the power series of the given function. give answer in sigma notation. All power series have center at 0. f(x)=(e^(-x)^2) -1+(x^2) and g(x)=x cos (x/square root 3)

### College Calculus (Binomial Series)

Expand f(x) = (x+x^2)/((1-x)^3) as a power series and use it to find the sum of series (SUM from n=1 to infinity) (n^2)/(2^n) PLEASE HELP.

### Integral Calculus

We can use this power series to approximate the constant pi: arctan(x) = (summation from n = 1 to infinity) of ((-1)^n * x^(2n+1))/(2n+1) a) First evaluate arctan(1) without the given series. (I know this is pi/4) b) Use your answer from part (a) and the power series to find a...

### Calculus

a) Find the Taylor series associated to f(x) = x^-2 at a = 1. Be sure to show the general term of the series. b) Find the radius of convergence of the series. c)Use Lagrange's Remainder Theorem to prove that for x in the interval of convergence with x > 1; the power series ...

### math power series(please helpassessment tomorrow)

The exponential function can be represented as an infinity power series as follows. e^x=1 + x/1! + x^2/2! + x^3/3!+⋯,-∞<x<∞ 1. Calculate e (which is the same as e^1) to 4 significant figures by using as many terms of the power series expansion as is necessary. Show...

### Calculus

This is going to be pretty hard to show as text since it would be easier for me to post a picture of the question. The question has f(x) = x/4^2 - (2x^3)/4^4 + (3x^5)/4^6 + ... . I am trying to find out the value of f(2). There is a hint to differentiate the power series ...

### calculus

With power series, is an endpoint convergent if you plug it back into the original series, and get an alternating series that is conditionally convergent?

### Calculus

does infinite power series -1/n diverge? (i think so, because it is just the negative of the harmonic series)...? thank you!

### Calculus II

(a) Use differentiation to find power series representation for f(x)=1/(1+x)^2 What is the radius of convergence? (b) Use part (a) to find a power series for f(x)=1/(1+x)^3 (c) Use part (b) to find a power series for f(x)=x^2/(1+x)^3 I found part (a) which was Σ n=0 to &#...

### calculus

Use division of power series to find the first three terms of the Maclaurin series for y = sec x.

### calculus

Use multiplication of power series to find the first three non-zero terms of the Maclaurin series of e^x ln(1 − x).

### Calculus - Taylor #2

Find the Taylor series for f(x) centered at the given value of 'a'. (Assume that 'f' has a power series expansion. Do not show that Rn(x)-->0.) f(x) = x3, a = -1 and what i've done so far: f (x) = x^3 f ' (x) = 3x^2 f '' (x) = 6x^1 f ''' (x) = 6x f (-1) = -1 f ' (-1) = 3 f...

### Calculus 2

The following function has a series of the form the sum from n=0 to infinity of c(subn)x^n. Calculate the coefficients c(subn) and express the power series in summation notation. f(x)=(pi*x)/(pi*x+1) Thank you so much for your help!!!!

### calculus

How would you determine the power series of 1/(1-x)^3. I know that the series of 1/(1-x) is x^n, but how would you manipulate it for this scenario?

### College Calculus

Suppose the series An (from n=1 to INF) is known to be convergent. Prove that series 1/(An) (from n=1 to INF) is a divergent series. I have no idea what to do... please help!

### power dissipation

What is the power dissipated by resistor R1 of the following circuit: two batteries in series (with values V1 = 20 volts and V2 = 20 volts) connected across three resistors in series with values R1 = 10k, R2 = 10k, and R3 = 20k im getting the answer 4 but i know its wrong. ...

### Calculus

What is the radius of convergence of the power series (((2n)!x^(n))/((2n-1)!)), and what is its interval of convergence? I used the ratio test and found that the radius of convergence is 0, as it is impossible for the absolute value of infinity to be less than 1. I am not sure...

### Calculus

Represent f(x)= (e^x -1)/x as a power series.

### calculus

use the power series to estimate the series: from 0 to 4 of ln(1+x)dx with absolute value of the error less than .0001/ Give your estimate of the integral as well as a bound on the error. I found the 'terms' in the series to be: x-(1/2)x^2+(1/3)x^3-(1/4)x^4...... with a radius...

### calculus

use the power series to estimate the series: from 0 to 4 of ln(1+x)dx with absolute value of the error less than .0001/ Give your estimate of the integral as well as a bound on the error. I found the 'terms' in the series to be: x-(1/2)x^2+(1/3)x^3-(1/4)x^4...... with a radius...

### Calculus

Hi, could someone please help me with this question? Thanks Calculate the Maclaurin series of f(x)=4x^3*sin(x^4). Explicitly use the Maclaurin series for sine. Using this series for f(x), verify that the integral of 4x^3*sin(x^4)dx=-cos(x^4)+C.

### calculus

write a power series for e to the 2x and find the interval of convergence

### math - calculus BC

find a power series representation of: f(x)=((x^2)-1)*sin(x)

### Physics

In a series circuit, the power source is 9-volt battery and three resistors. R1=7ohm R2=9ohm R3=2ohm What is the total resistance in this series circuit? What is the current? Please help I don't understand this!, Thank you

### Calculus

If S1 = 0.7 and S2 = 2.1 in geometric series, what would the sum of the first 12 terms in the series be? I tried doing this, and I got 1.16 or something :S How exactly do I do this? Please tell me what formula to use. I was using the Sn = a(rn-1)/r-1

### Calculus

By recognizing each series below as a Taylor series evaluated at a particular value of x, find the sum of each convergent series. A) 1+5 + (5^2)/(2!)+(5^3)/(3!)+(5^4)/(4!)+...+ (5^k)/(k!)+...= B) 1-(2^2)/(2!)+(2^4)/(4!)-(2^6)/(6!)+...+((-1)^(k)2^(2k))/((2k)!) +...=

### Calculus - - Reiny

If S1 = 0.7 and S2 = 2.1 in geometric series, what would the sum of the first 12 terms in the series be? I tried doing this, and I got 1.16 or something :S How exactly do I do this? Please tell me what formula to use. I was using the Sn = a(rn-1)/r-1

### Calculus 2

Determine the first three terms of the power series representations for the following functions: a) 2/(1+x)^3 b) 1/1+x^2 c) ln(1+x)

### Integral Calculus - Series

Find if series is convergent or divergent. Series from n=2 to infinity (4n+7)/(3n^3 -8n)

### Calculus 2

Calculate c(sub0), c(sub1), c(sub2), c(sub3), and c(sub4) for the power series the sum from n=0 to infinity of c(subn)x^n that represents f(x)=tanx. Use the first two nonzero terms of the series to approximate the tangent of 1/4 radian. Compare your approximation with the ...

### Calculus

Determine the following about the series. Indicate the test that was used and justify your answer. Sigma (lower index n = 1; upper index infinity) [sin((2n-1)pi/2)]/n A. The series diverges B. The series converges conditionally. C. The series converges absolutely. D. It cannot...

### Calculus

Consider the infinite series of the form: (+/-)3(+/-)1(+/-)(1/3)(+/-)(1/9)(+/-)(1/27)(+/-)...(+/-)(1/3^n)(+/-)... (A) Find x and y from: x(</=)(+/-)3(+/-)1(+/-)(1/3)(+/-)...(</=)y. (B) Can you choose the signs to make the series diverge? (C) Can you choose the signs to ...

### calculus

Consider the infinite series of the form: (+/-)3(+/-)1(+/-)(1/3)(+/-)(1/9)(+/-)(1/27)(+/-)...(+/-)(1/3^n)(+/-)... (A) Find x and y from: x(</=)(+/-)3(+/-)1(+/-)(1/3)(+/-)...(</=)y. (B) Can you choose the signs to make the series diverge? (C) Can you choose the signs to ...

### calculus

Consider the infinite series of the form: (+/-)3(+/-)1(+/-)(1/3)(+/-)(1/9)(+/-)(1/27)(+/-)...(+/-)(1/3^n)(+/-)... (A) Find x and y from: x(</=)(+/-)3(+/-)1(+/-)(1/3)(+/-)...(</=)y. (B) Can you choose the signs to make the series diverge? (C) Can you choose the signs to ...

### Calculus!!!

I need your help... I've posted this question a while ago but no one has answered it yet. Please please help me. Which of the following series can be used to compute ln(.8)? a) ln(x-1) expanded about x=0 b) lnx about x=0 c) ln x in powers of (x-1) d) ln(x-1) in powers of (x-1...

### Calculus

How can I prove this series alternating series converges(this is the answer)? (-1)^2*(2/3)^n I tried it this way: an = (2/3)^n, then i just broke it down. 2^n/(3^n) and i took the ratio of it and got 2/3 which does not equal to one which would mean the series diverges.. but ...

### calculus repost, please assist pleassssssse

Hi Trying to work with confusing Taylor series....any assistance would be much appreciated!! How can I use T(x)=5-9((x-2)^2)-3((x-2)^3) to approximate the f(0) ???? I realize that Taylor series f(x)=f(a)+f'(a)(x-a)+f''(a)((x-a)^2)etc... but the above T(x) is centered at x=2, ...

### Pre-Calculus/Calculus

I am too embarassed to ask this Calculus (really pre-calculus) question in tutoring, because I know I should know. Is the inverse of f(x)=3x-1 actually f(x)=1/3x+1? How do I find it? What if it asks the same equation replaced with f to the -1 power (x)? I think I know how the ...

### Pre-Calculus

Q.Determine the sum of each infinite geometric series. t_1= 8 r = -2^1/2 ---------------------------------------- A.This is a divergent series because the absolute value of r is greater than 1. ---------------------------------------- Q. The first term of an infinite geometric...

### calculus

Consider ∞ ∑ [(3k+5)/(k²-2k)]ᵖ, for each p ∈ ℝ. k=3 Show this series { converges if p > 1 { diverges if p ≤ 1 Hint: Determine the known series whose terms past the second give an approximate match for the terms of this series. This ...

### Algebra 2

I need steps on how to complete this please i am so confused and lost. :( Consider the infinite geometric series x e n=1 -4(1/3) n-1. In this image, the lower limit of the summation notation is "n=1". a. Write the first four terms of the series. b. Does the series diverge of ...

### Calc

We are working on finding the intervals of convergence of power series in class. Why do we not have to test for the convergence of the endpoints for geometric series? They always seem to diverge. Is this a set rule when working with the geometric series for this type of problem?

### college differential equations

Find two linearly independent power series solutions to the diffrential equation. State the first 3 therms of each series: 2x^2y''+xy'-(1+2x^2)y=0

### Calculus

Obtain the MacLaurin series for 1/(2-x) by making an appropriate substitution into the MacLaurin series for 1/(1-x). ------------ The MacLaurin series for 1/(1-x) = Σ x^k I substitue (x-1) in for x, because 1/(2-x) = 1/(1-(x-1)) Making the same substitution in the ...

### Calculus - series

I'm getting this answer wrong, can someone please help show me what i'm missing?? thank you :) Infinity of the summation n=0: [(-1)^n pi^(2n)] / [6^(2n) (2n)!] this is my work: [(-1^0) pi^(2*0)] / [6^(2*0) (2*0)!] + [(-1^1) pi^(2*1)] / [6^(2*1) (2*1)!] + [(-1^2) pi^(2*2)] / [6...

### calculus

let f be the function f(x) = e^(2x^2) find the first four nonzero terms and the general term of the power series for f(x) about x = 0 i tried doing this problem but finding the derivatives gets way too complicated can anyone help??

### calculus

in the following series x is a real number. In each case use the ratio test to determine the radius of convergence of the series. Analyze the behavior of the series at the endpoints in order to determine the interval of convergence. A) (nx^n)/(n^2 + 2) B)((n^2)(x-2)^n)/2^n C...

### Calculus Help Please

Hello! I am struggling with this problem: Find the Taylor Series for sin(x-2) centered at c=3. My work so far: sin(1)+(x-3)cos(1)-(1/2)(x-3)^2sin(1)-(1/6)(x-3)^3cos(1)+(1/24)(x-3)^4sin(1)... I know that the Taylor series for sign is typically: the summation from n=0 to ...

### algebra, series

The sum of the first n terms of a series is 1-(3/4). Obtain an expression for the nth term of the series. Prove that the series is geometric, and state the values of the first term and the common ratio. Please show workings

### ASAP

can someone please make up an address and a phone number that i can use for my brochure? please. please. ASAP

### Math

Hey, I just need my answer checked. Simplify: y to the 4th power times y to the 3rd power y to the 1st power y to the 7th power ** y to the 12th power y to the 43rd power correct? If not, please show work for me. thanks.

### calc

f(x)=x^2/4+x^3 find the power series representation...so far i found ...Óx^2n+2/4^n...is dat correct?...nd then it is asking to find the radius and interval of convergence...i found the radius to be x^2/4...so i set the radius between -1 and 1...nd then solve for x...i got x ...

### CALCULUS-URGENT

find the radius and interval of convergence for the series the series from n=0 to infinity of ((-1)^n*x^n)/(n+1)

### CALCULUS

find the radius and interval of convergence for the series the series from n=0 to infinity of ((-1)^n*x^n)/(n+1)

### Calculus 2

Hello, I don't know what test to use for this series: Determine the sum of the following series: inf E n=1 (2^n + 9^n) / 12^n thank you!

### CALCULUS-URGENT- no one will respond!!!

find the radius and interval of convergence for the series the series from n=0 to infinity of ((-1)^n*x^n)/(n+1)

### Calculus, series

I cannot figure this out! What is the series (the Pattern) of this sequence? {1,5,1,5,1,5,1,5.......}

### calculus

how do you find the sum of a series? for example: the series from n=0 to infinity of (-1)^n/n!??? thanks

### diffrential equations

Find two linearly independent power series solutions to the diffrential equation. State the first 3 therms of each series: 2x^2y''+xy'-(1+2x^2)y=0

### calculus

I need help understanding how the series of e derives into the exponential series using the binomial theorem. Here is a link to a pic of a page in my book, regarding the exponential series: ht tp://i46.tiny pic(.)(com)/qz0oat . jpg (remove parentheses and spaces) A couple of ...

### phsyics

A light bulb rated by the manufacturer as using and average power of 128.0 W when connected to a 73.0 Hz power source having a maximum voltage of Vmax = 189 V (the effective voltage under these conditions is what is called RMS voltage and is Vrms = 133.6 V), is connected in ...

### Calculus

If 2 to the 1998 power - 2 to the 1997 power - 2 to the 1996 power + 2 to the 1995 power = k times 2 to the 1995 power, what is the value of k? (A) 1 (B) 2 (C) 3 (D) 4 (E) 5

### Calculus

Show that the following series is absolutely convergent: Summation from 1 to infinity: [(-1)^n * (n+1) * 3^n]/ [2^(2n+1)] I've done the ratio test and replaced n in this series with n+1. I get 3/4 in the end, which is less than 1, which confirms that the series is abs. ...

### calculus

i have to determine whether the series is convergent, and if, find the sum the series is from k=1 to infinity of 2/((k+1)(k+3)) I got 5/6 as my answer and didn't know if it was right...

### calculus

what does this series, if it converges, converge to? the series from n=1 to infinity of (2^n + (-1)^n)/3^n

### math

How do prove without using a formula , that the sum of the series 3²+3³+3to the power of 6+...to 20 terms is given by S20 =9/8(9to the power of 20 -1)

### Calculus

Hi, I am trying to find a closed form for the power series from n=2 to infinity of x^n/(n-1)n. I'm not really sure how to do this- I found the first and second derivatives which were x^(n-1)/(n-1) and x^n-2. However, this didnt really seem to help much. Any help is appreciated!

### Math

A series of 288 consecutive odd integers has a non-zero sum that is a perfect fourth power. Find the smallest possible sum for this series.

### Calculus (PLEASE HELP ASAP!)

Find f(x) satisfying the given conditions: 1) f"(x) = 1/x^3 f'(1) = 1/2 f(1) = 0 2) f"'(x) = sin (x) f"(0) = 0 f'(0) = 1 f(0) = 0

### chemistry

Hydrogen exhibits several series of line spectra in different spectral regions. For example the Lyman series (nf = 1 in Balmer-Rydberg equation) occurs in the ultraviolet region while the Balmer (nf = 2) series occurs in the visible range and the Paschen (nf = 3), Brackett (nf...

### Calculus

The divergence test applied to the series ∑n=1 to ∞ 3n/(8n+9) tells us that the series converges or diverges? I got that it was divergent because it was undefined at infinity, is my answer right?

### calculus

Find the indefinite integral of 1-tanx/1+tanx Dont know how to really approach this question. Should i use identities, or is there a power series i can use?

### Calculus Test Question ASAP

The graph of y = cos x is concave down on which interval? (-pi,0)??????? please help!!!!

### Calculus please help

The power, P, dissipated when a 6-volt battery is put across a resistance of R ohms is given by P=36R. What is the rate of change of power with respect to resistance?

### Physics

A circuit consists of a resistor of R=7 Ω, a capacitor of C=7 μF, and an ideal self-inductor of L=0.04 H. All three are in series with a power supply that generates an EMF of 5sin(ωt) Volt. The internal resistance of both the power supply and the inductor are ...

### Calculus 2 - Series

I am so confused on how to do series problems...especially these. How can you tell the pattern and determining the formula for them? Can someone please help? 26) Write the first five terms of the sequence {an} whose nth term is given. an = (n + 3)/(2n − 1) a1 = ? a2 = ? ...

### Calculus

Please.... I need your help! I posted this question yesterday and no one has answered it yet. Can anyone help me please? My question was: The Taylor series about x=5 for a certain function f converges to f(x) for all x in the interval of convergence. The nth derivative of f at...

### algebra

Please help I have tried this question so many times: I cannot type out the exponents because my keyboard does not allow so I'll have to write it in verbal form I'm sorry. What is the simplified form of -9 m to the power of negative two times n to the power of 5 times 2 m to ...

### Calculus 2 (Series)

Can anyone help me start this problem from beginning to end, along with explanations on how to go about the problem for a better understanding how to do this series problem? 1) Find the values of p for which the series is convergent. Summation notation symbol (with n=1 on ...

### Health

1 Select the skill-related component which is defined as the ability to perform a combination of movements with different parts of your body? A-Balance B-coordination*** C-power D-speed Please help! ASAP!

### Please answer my Misc. Question Asap!!!!!!!!

asap!!!!!!!!!! How rude. We are volunteers, and adults.

### electrical

6.A resistor R1 dissipates power P when connected to a certain generator with voltage V. If a resistance R2 is put in series with R1 the power dissipation by R1 A) Decreases B) Increases C) Remains the same D) Any of the above depending upon the value of R1 and R2

### calculus

test the series for convergence or divergence the series from n=0 to infinity of (x^2+1)/(x^3+1) I said that due to the limit comparison test this converges at 1

### calculus

test the series for convergence or divergence the series from n=0 to infinity of sin (2^-x) I wasn't sure what test to use to see if this was or wasn't convergent

### calculus

determine whether the series is convergent if so find sum it is the sum from k=1 to infinity of ((-1)^k)/(3^(k+1)) i found this series to be geometric where a=-1/9 and r=1/3 my answer was converges to 1/6

### calculus

test the series for convergence or divergence using the alternating series test the sum from n=1 to infinity of (-1)^n/(3n+1) I said it converges, is this true?

### calculus

test the series for convergence or divergence using the alternating series test the sum from n=1 to infinity of (-1)^n/(3n+1) I said it converges, is this true?

### calculus

Show that the series(−1)^n−1(bn) where bn = 1/(n^1/2) if n is odd and bn = 1/2^n if n is even, diverges. Why does the alternating series test fail?

### Solar Energy Help ASAP

John has used a solar simulator setup to measure the relation between the voltage and the current of a small photovoltaic cell (40 cm long and 40 cm wide). The measurement setup maintains the standard measurement conditions: the temperature is controlled to 25oC, the incident ...

### calculus

Another problem: determine whether the series is convergent if so find sum it is the sum from k=1 to infinity of ((-1)^k)/(3^(k+1)) i found this series to be geometric where a=-1/9 and r=1/3 my answer was converges to 1/6

### Pre-calculus

Which of the following series is divergent? a) 1+3(1/4)+9(1/4)^2+27(1/4)^3... b) 1+3(1/5)+9(1/5)^2+27(1/5)^3... c) 1+3(1/7)+9(1/7)^2+27(1/7)^3... d) 1+3(1/2)+9(1/2)^2+27(1/2)^3... How do you determine if a series in convergent or divergent??? The book that I have is about as ...

### Calculus

If you have a geometric alternating series, and you prove that the series is converging by doing geometric series test, and NOT alternating series test, then does that allow you to say that the series converges ABSOLUTELY? Or should you do alternate series test also to say ...

### calculus

for each series determine if the series is absolutely convergent and convergent the sum from 0 to infinity of (-1)^n/(the square root of (n+1))

### calculus

test the series for convergence or divergence the series from n=1 to infinity of 1/(arctan(2n)) I again didn't know what test to use

### Math

Need to simplify (6b to the 2 power)to the 2nd power (6b to the 4th power)to the 4th power equals 24b to the 4th power Not sure if I did this right trying to understand how to simplify. Please help, please.

### calculus

does this series converge, and if so is it absolutely convergent? the series from n=1 to infinity of ((-1)^*n+1))/n^4 I found that by the ratio test it was inconclusive, so no abs. conv is this right? and how do i know if it is simply convergent?