Part A
Part B
In this exercise, you may assume that the integration of the infinite sum can be done term-wise.
Homework Answers
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Part A
Part B
In this exercise, you may assume that the integration of the
infinite...
(a) Evaluate the double integral 4. (sin cos y) dy dr. Hint: You may need the formula for integration by parts (b) Show...
(a) Evaluate the double integral 4. (sin cos y) dy dr. Hint: You may need the formula for integration by parts (b) Show that 4r+6ry>0 for all (r,y) ER-(x,y): 1S2,-2Sysi) Use a double integral to compute the volume of the solid that lies under the graph of the function 4+6ry and above the rectangle R in the ry-plane. e) Consider the integral tan(r) log a dyd. (i) Make a neat, labelled sketch of the region R in the ry-plane over...
Exercise 2 (Monte Carlo integration). Let (Xk)kzl be i.i.d. Uniform([0, 1]) RVs and let f: [0,1]...
Exercise 2 (Monte Carlo integration). Let (Xk)kzl be i.i.d. Uniform([0, 1]) RVs and let f: [0,1] -- R be a continuous function. For each n2 1, let (f(X)f(X2).+f(Xn)) (3) In = -- .. + Sof(x) dx in probability. (i) Suppose o f (x)| dx (ii) Further assume that f lf(x)2 dx <o0. Use Chebyshef's inequality to show that :< oo. Show that In P (IIn-I2 alVnVar(f(X1)) a2 f(x)2 dx (4)
Thank you! Exercise 33: (How good are your integration skills?) Let m E N. Show that 2772)! (ech()a π 2m+1 and cosh(...
Thank you!
Exercise 33: (How good are your integration skills?) Let m E N. Show that 2772)! (ech()a π 2m+1 and cosh(z) = 2e+ e-*), x E R. (z) = cosh(x) a) Make a change of variables such that 0 Hint: You may use that sech : [0.00) → (0, 1] is invertible with-sech-1(r) b) Make a change of variables such that c) Show that π 2772)! 2ml :- (2mm!)2 2 To do so, you may show that m- PrL...
1. a) Find using integration by parts. Does the improper integral converge? b) What can you...
1. a) Find
using integration by parts. Does the improper integral
converge?
b) What can you say about the infinite series
using the improper integral in the previous part? Estimate the
partial sum S100 =
. Find upper bound for R100 =
and use the integral test.
We were unable to transcribe this imagepinsinity In(x)}dz We were unable to transcribe this image100 In(n) 2 73 n=101
hiques illustrated in this section are designed to transform or si fore you apply a specific...
hiques illustrated in this section are designed to transform or si fore you apply a specific method. In fact, these ideas may help you recognize nod to use. Keep them in mind as you learn new integration methods and improve gration skills. eral Practice Exercises 7-64. Integration review Evaluate the following integrals. (3 - 5x)* 8. (9x - 2) dx 7. l dt 1) first.) sin’x dx? to show that 11. Sin 24 de Late 14. lo + 32 +...
The period T of a pendulum with length L meters that makes a maximum angle of...
The period T of a pendulum with length L meters that makes a maximum angle of θ0 with the vertical is The vertical is: T= 4\sqrt{\frac{L}{9}}\int _0^{\frac{\pi }{2}}\frac{dx}{\sqrt{1-k^2sin^2x}} where k=sin((1/2)θ0) and g=9.8 m/sec2 in the acceleration due to gravity. (a) Find the first four terms of a series expansion for T by expanding the integrand using the binomial series and integrating term by term (your answer will include L, g, k). You may use the following integration fact: The integration...
1. Use the Limit Comparison Test to prove that the series S(a, b) converges unless a or b is a negative integer. Why must this restriction on a and b be imposed? 2. In all that follows we assume with...
1. Use the Limit Comparison Test to prove that the series S(a, b) converges unless a or b is a negative integer. Why must this restriction on a and b be imposed? 2. In all that follows we assume without losing generality that a >b. Use partial fractions to show that 3. To get warmed up, write the first few terms of the series S(1,0) k(k + I )-4 k--J . Write the nth term of the sequence of partial...
please do a,b,c,d, j, k ,m ,r,s Exercise 5.12. Determine whether the infinite series is convergent,...
please do a,b,c,d, j, k ,m ,r,s
Exercise 5.12. Determine whether the infinite series is convergent, of vergent. Show your reasoning. In particular, make clear which of the several available tests you are using. X 0 ΣΠΗ3 ο Στη + 1)(n + 3) 4) Στ+6 η2 + 5η +6 Stainle 3( +1)/2 4ก 2 10” 8 80 81 82 8 ก+ 7 ๑int 18 ปี 2) ") oth) 18 มี 18 ก ! Exercise 5.12. Determine whether the infinite series...
Please answer all questions, and I will rate you well! Thanks :) 2. 12/18 points | Previous Answers SCalcET8 6.4.013.MI My Note A heavy rope, 60 ft long, weighs 0.5 lb/ft and hangs over the edge of a...
Please answer all questions,
and I will rate you well! Thanks :)
2. 12/18 points | Previous Answers SCalcET8 6.4.013.MI My Note A heavy rope, 60 ft long, weighs 0.5 lb/ft and hangs over the edge of a building 150 ft high. (Let x be the distance in feet below the top of the building. Enter xas x,.) (a) How much work W is done in pulling the rope to the top of the building? Show how to approximate the...
(a) Evaluate the double integral 4. (sin cos y) dy dr. Hint: You may need the formula for integration by parts (b) Show that 4r+6ry>0 for all (r,y) ER-(x,y): 1S2,-2Sysi) Use a double integral to compute the volume of the solid that lies under the graph of the function 4+6ry and above the rectangle R in the ry-plane. e) Consider the integral tan(r) log a dyd. (i) Make a neat, labelled sketch of the region R in the ry-plane over...
Exercise 2 (Monte Carlo integration). Let (Xk)kzl be i.i.d. Uniform([0, 1]) RVs and let f: [0,1] -- R be a continuous function. For each n2 1, let (f(X)f(X2).+f(Xn)) (3) In = -- .. + Sof(x) dx in probability. (i) Suppose o f (x)| dx (ii) Further assume that f lf(x)2 dx <o0. Use Chebyshef's inequality to show that :< oo. Show that In P (IIn-I2 alVnVar(f(X1)) a2 f(x)2 dx (4)
Thank you!
Exercise 33: (How good are your integration skills?) Let m E N. Show that 2772)! (ech()a π 2m+1 and cosh(z) = 2e+ e-*), x E R. (z) = cosh(x) a) Make a change of variables such that 0 Hint: You may use that sech : [0.00) → (0, 1] is invertible with-sech-1(r) b) Make a change of variables such that c) Show that π 2772)! 2ml :- (2mm!)2 2 To do so, you may show that m- PrL...
1. a) Find
using integration by parts. Does the improper integral
converge?
b) What can you say about the infinite series
using the improper integral in the previous part? Estimate the
partial sum S100 =
. Find upper bound for R100 =
and use the integral test.
We were unable to transcribe this imagepinsinity In(x)}dz We were unable to transcribe this image100 In(n) 2 73 n=101
hiques illustrated in this section are designed to transform or si fore you apply a specific method. In fact, these ideas may help you recognize nod to use. Keep them in mind as you learn new integration methods and improve gration skills. eral Practice Exercises 7-64. Integration review Evaluate the following integrals. (3 - 5x)* 8. (9x - 2) dx 7. l dt 1) first.) sin’x dx? to show that 11. Sin 24 de Late 14. lo + 32 +...
1. Use the Limit Comparison Test to prove that the series S(a, b) converges unless a or b is a negative integer. Why must this restriction on a and b be imposed? 2. In all that follows we assume without losing generality that a >b. Use partial fractions to show that 3. To get warmed up, write the first few terms of the series S(1,0) k(k + I )-4 k--J . Write the nth term of the sequence of partial...
please do a,b,c,d, j, k ,m ,r,s
Exercise 5.12. Determine whether the infinite series is convergent, of vergent. Show your reasoning. In particular, make clear which of the several available tests you are using. X 0 ΣΠΗ3 ο Στη + 1)(n + 3) 4) Στ+6 η2 + 5η +6 Stainle 3( +1)/2 4ก 2 10” 8 80 81 82 8 ก+ 7 ๑int 18 ปี 2) ") oth) 18 มี 18 ก ! Exercise 5.12. Determine whether the infinite series...
Please answer all questions,
and I will rate you well! Thanks :)
2. 12/18 points | Previous Answers SCalcET8 6.4.013.MI My Note A heavy rope, 60 ft long, weighs 0.5 lb/ft and hangs over the edge of a building 150 ft high. (Let x be the distance in feet below the top of the building. Enter xas x,.) (a) How much work W is done in pulling the rope to the top of the building? Show how to approximate the...
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