A pply Taylor's s expansion and find the se yies for tann at = 4 %3D

Q: Series to Rind use lim 1- Cos 2X

A: Use series expansion of the e3x and cos 2x with help of ex and cos x:

Q: /tangent slupe rosin (20) when 5 2) 553 る 653 O not of thc above

A:

Q: et Determine if the improper integral dx converges or diverges. (1 - e)2 If it converges, find its…

A:

Q: Ise the series to evaluate the limit tan-1 y – siny lim y→0 y³cosy

A:

Q: Use series to approximate the definite integral I to within the indicated accuracy. 6x cos(x4) dx…

A: To evaluate:

Q: Evaluate the integrals in Exercises

A: ∫-ln20cosh2x2dx∫0ln104sinh2x2dx

Q: Find hale reange Sine series Ex 2 (odd fourier sseries) For the function

A: Given function is: f(x)=x, 0<x<π2π2, π2<x<π Here, L=π f(x)=∑n=1∞bnsin(nx), where…

Q: Determine maximum error between 0 ≤ ? ≤ ?/3 interval for fourth degree Taylor expansion of ?(?) =…

A: Determine maximum error between 0 ≤ ? ≤ ?/3 interval for fourth degree Taylor expansion of ?(?) =…

Q: Exaumple- Find the half pervodic Punetion which dé finition in rary expansion for the period as :.…

A:

Q: Use series to evaluate the limits

A:

Q: x° e* dx 00

A: Given : ∫-∞0x5exdx

Q: Use power series to approximate the integral to four decimal places. 1/2 arctan(x?) dx

A: Given :      Function y=∫01/2arctan(x2)dx                          =∫01/2tan-1(x2)dx      tan-1x…

Q: Determine whether it converges or diverges. You must provide justification for your answer. |…

A: Answer is yes its convergent .

Q: 1 Find the mean value over the interval [0,2n]. 4+cosx

A:

Q: The area under the graph of the function e−x^2   (natural exponent e to the -x squared) plays an…

A:

Q: Using e and e expansions, find sinh x.

A:

Q: Evaluate the following improper integral if it is convergent. 00 10 dx x In x Select the correct…

A: Given information:          The integral is ∫2∞10x ln xdx  Calculation: The integral will converge…

Q: Use series to approximate the definite integral S xcos(x²)dx . (Give your answer correct to 10-3)

A:

Q: Solve the following improper integral. State whether the integral converges, or diverges. If it…

A: To state whether the given improper integral converges or diverges ∫4∞1x3dx

Q: Evaluate the indefinite integral as an infinite series. / arctan (a") de

A:

Q: 6) Using gamma function, evaluate So 6 хе 2x dx

A: Introduction: Gamma function is an integral function that is defined through an integration. The…

Q: (b). S cos (logx)dx. COS

A:

Q: QUESTION 3 Determine the convergence of the integral tan r J, In(cos r))? dr. UTM UTM

A: We have to find the given integral is convergent or divergent.

Q: What is the area of the region between the sine curve and the x-axis from to 2 ? -1 2 1 4 3.

A: Here we have to find the area of the region bounded by the sine curve and the x-axis from π2 to 2π.…

Q: (a) |r cos(a*)dz

A: As per our guidelines we are supposed to answer only first part. Kindly repost other parts in the…

Q: -dx converges or diverges. Justify your claim. determine if the integral 1+ cos? r

A: Introduction: When the integrand becomes discontinuous at any of the limits of the given…

Q: Use series to approximate the definite integral I to within the indicated accuracy. dr. Jerror…

A: Given I=∫00.8x31-x3+x62-x96+.......dx we know that ex=1+x+x2+..........…

Q: 9) Determine whether the following integral is divergent or convergent and, if convergent, evaluate…

A:

Q: * Use time series to approximate the Value of the integrals, Calculate the Birst thriee terms. 1- Cメ

A: You have posted multiple questions. As per norm, we will solve only the first question as nothing is…

Q: Expand fix)= Si (x+ T),O<x< I ina half Yange sine series

A: We use the half range sine series formula to find the solution given as follows:

Q: pres ms of sums and 1. log, 6xy°z* 2. log 3. In 4. log vrt 5. loga

A: We have to simplify given log  expression into sum or  difference.

Q: use Series to evaluale lim sinhx²- x 2 メー→ メ Cos x 3.

A:

Q: e-a dx.

A: COMPARISON TEST

Q: What is wrong with this calculation? 1 dx In |x||, = In 1 - In 1 = 0 - 1

A: The integral of 1xwith respect to x is log(|x|). where x≠0, cause if it is zero then function became…

Q: Evaluate the indefinite integral as an infinite series. | arctan(x2) dx Σ + C n = 0

A: Answer

Q: Evaluate the following improper integral if it is convergent. 6 dx x In x Select the correct choice…

A: Given:          ∫2∞6x lnxdx

Q: 1 ) *It can be shown that the improper integral e sin xdx =. Can we conclude that 2 Le" sin n…

A: Integral test

Q: 6. Evaluate the indefinite integral as an infinite series. (b) / sin z (a) / r cos(r)dr

A:

Q: Prove the identity (cosh x + sinh x) n  = cosh n  x + sinh nx

A: Consider the given L.H.S of the given identity coshx+sinhhxn

Q: Evaluate the following improper integral if it is convergent. S 13 -dx x In x Select the correct…

A: The main objective is to check the value of the integral ∫2∞13xln xdx.

Q: f(x) = sinh x cos x,-n <x< n. ometric series.

A: fx=sinh x cos x , -π≤x≤π P is periodic of period 2π fx+2π=fx   sinx+2πcosx+2π=sinh x cos x  cosx…

Q: a. Prove that ƒ(x) = x - ln x is increasing for x&gt; 1. b. Using part (a), show that ln x &lt; x if…

A: The domain of f(x)is all positive real numbers. Find the first derivative of f(x) to find whether…

Q: Use the Simpson's rule to estimate dx with n =4

A: Simpson's rule: ∫abfx dx≈∆x3 fx0+4fx1+fx3+⋯+2fx2+fx4+⋯+fxn where ∆x=b-an.

Q: converges or div rge 2n+ Sinln)

A: The given series is  ∑n=1∞ 12n+sinn We have to check whether the series converges or diverges.

Q: Evaluate the following definite integral. arctan dx

A:

Q: Evaluate the indefinite integral as an infinite series. 8. COS I dr

A: Note : As per our guidelines we are supposed to answer only one question. Kindly repost other…

Q: Evaluate the indefinite integral as an infinite series. arctan(x5) dx Σ( |)•c n = 0

A:

Q: special fomtion o Show thal (27)

A: We use Gamma function to prove the given result.

Q: sin dæ

A: