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1. In the first part of this question you will give three different proofs of the following equat...
In the first part of this question you will give three different proofs of the following equation...
In the first part of this question you will give three different proofs of the following equation: --(arctanh (r)) = 1-2 (a) (i) Use implicit differentiation to prove that equation (*) holds. (ii) Use the definition of arctanh (x) via the logarithm (see p. 106 of the Lecture notes) to prove that equation () holds. (ii) Use integration to prove that equation () holds. b) Using equation () from Part (a) find the indefinite integral J-alog (x)
In the first...
Find fY(y) from the domain: Consider the domain D={(x,y): 0 < x < 1,-x < y < x} and let fix, y)=cx,where c is a constant. 1.1 (4.6 marks) To start with, we wish you to determine c such th...
Find fY(y) from the domain:
Consider the domain D={(x,y): 0 < x < 1,-x < y < x} and let fix, y)=cx,where c is a constant. 1.1 (4.6 marks) To start with, we wish you to determine c such that f(x, y) a joint density of random vector (X, Y) that takes values on D. order to do that, you must first calculate fix, y) dA where dA is an area element of D, and then deduce c Hence you...
Please show work clearly! will give a thumbs up! 3. ( Practice ) Our goal is...
Please show work clearly! will give a thumbs up!
3. ( Practice ) Our goal is to find the arc length of the spiral r = 0 from 0 <O<1. (a) Using techniques from Trigonometric Integrals, show that the following integral equality holds: I sec r tandx = = / secx dx - Insec +tangl. 1/4 0 (b) Using Integration By Parts and part (a), evaluate secs x dx. Hint: let u = sec. in the IBP. (c) Use the...
Q1. DELTA FUNCTIONS! a) Calculate the following integrals, assuming c=2 in all parts! In part iv,...
Q1. DELTA FUNCTIONS! a) Calculate the following integrals, assuming c=2 in all parts! In part iv, assume the volume V is a sphere of radius 1 centered on the origin, and the constant vector ro = (0,3,4) c 8(x-c)dx (Hint: watch out for limits of integration. Remember, c=2 throughout) 8(x-c)dx iii) Sºx-cl 8(2x)dx (Hint: see Griffiths Example 1.15) iv) SS ir-r, 8(r)dr v) M F-F, P 8°(27)di (Hint: 8' () = 8(x)O(y)8(z)) b) Evaluate the integral ſ (1+e") ( )dt...
Q1: Give a bijective proof of the following identity E (%) = 2:1 using the following...
Q1: Give a bijective proof of the following identity E (%) = 2:1 using the following steps: (a) Use binomial paths represented as sequences (or tuples) of steps to define a set 24 representing the left-hand side. (b) Define a set Nr representing the right-hand side as a certain set of tuples with entries from the set {0,1}. (c) Define a bijective function I : 124 + S2R. (d) Show that your function in (c) is well defined. (There is...
Calculus 1 MAT 201 Final Exam, Spring 1 2019, LAGCC Evaluate the following limits, you may...
Calculus 1 MAT 201 Final Exam, Spring 1 2019, LAGCC Evaluate the following limits, you may use L'Hospital's rule, if it applies. -V31+4 lim 4-1 -4 a. b. Evaluate the following limit. lim xIn x x-0 2. Evaluate and explain your answer -xsin(x)+cos (x) x+1 130 dx (a.) 130 Differentiate each of the following below using the fundamental theorem of calc part 1 X cos? (1- 51) dt ) g (x) = S_ e (2c) g(t)= J x2t+1 3 Use...
You will integrate the following rational function: -222–162+36 dz (2-3) (x+2)(x-1) -222-162+36 To do this, start...
You will integrate the following rational function: -222–162+36 dz (2-3) (x+2)(x-1) -222-162+36 To do this, start by writing (2-3)(2+2)(x-1) A + В. 2+2 + C 2-1 1-3 (a) Put the right-hand side over a common denominator. Enter the numerator of the result. (b) Expand the numerator. It is a quadratic in z, which must equal the numerator of the original function. By equating the coefficients you should be able to formulate linear equation in A, B and C. In each...
For this assignment, you submit answers by question parts Assignment Scoring Your best submission f...
For this assignment, you submit answers by question parts Assignment Scoring Your best submission for each question part is used for you O-1 points SCalcET8 7.1.513.XP 7. Evaluate the integral. 1 ydy e5y Jo Need Help? Watch It Tal Read It Save Progress Practice Ano Submit Answer e Assignment Submission For this assignment, you submit answers by question parts. The nu Assignment Scoring Your best submission for each question part is used for your score 0 -1 points SCalcET8 7.1.030...
Part II: Short answer (5 pts. each) Give a short answer to the following questions (1-3 sentences and/or a brief sketch) Make a crude sketch of the world line of a particle initially at rest which th...
Part II: Short answer (5 pts. each) Give a short answer to the following questions (1-3 sentences and/or a brief sketch) Make a crude sketch of the world line of a particle initially at rest which then accelerates in the-x direction for a short time, then travels at constant velocity. 1. What is the relation between decay constant and half-life? Prove this relation with a few lines of algebra. If needed, start with the formula mentioned in Essay #1, below....
Consider the following differential equation Note: For each part below you must give your answers in terms of fract...
Consider the following differential equation Note: For each part below you must give your answers in terms of fractions (as appropriate), not decimals (a) The above differential equation has a snaar point at x 0 . It the singular point at x-0 is a regular singular point, then a power series for the solution y(x) can be lound using the Frobenius method. Show that x = 0 is a regular sigar point by calculating: xp(x) = y(x) = Since both...
In the first part of this question you will give three different proofs of the following equation: --(arctanh (r)) = 1-2 (a) (i) Use implicit differentiation to prove that equation (*) holds. (ii) Use the definition of arctanh (x) via the logarithm (see p. 106 of the Lecture notes) to prove that equation () holds. (ii) Use integration to prove that equation () holds. b) Using equation () from Part (a) find the indefinite integral J-alog (x)
In the first...
Find fY(y) from the domain:
Consider the domain D={(x,y): 0 < x < 1,-x < y < x} and let fix, y)=cx,where c is a constant. 1.1 (4.6 marks) To start with, we wish you to determine c such that f(x, y) a joint density of random vector (X, Y) that takes values on D. order to do that, you must first calculate fix, y) dA where dA is an area element of D, and then deduce c Hence you...
Please show work clearly! will give a thumbs up!
3. ( Practice ) Our goal is to find the arc length of the spiral r = 0 from 0 <O<1. (a) Using techniques from Trigonometric Integrals, show that the following integral equality holds: I sec r tandx = = / secx dx - Insec +tangl. 1/4 0 (b) Using Integration By Parts and part (a), evaluate secs x dx. Hint: let u = sec. in the IBP. (c) Use the...
Q1. DELTA FUNCTIONS! a) Calculate the following integrals, assuming c=2 in all parts! In part iv, assume the volume V is a sphere of radius 1 centered on the origin, and the constant vector ro = (0,3,4) c 8(x-c)dx (Hint: watch out for limits of integration. Remember, c=2 throughout) 8(x-c)dx iii) Sºx-cl 8(2x)dx (Hint: see Griffiths Example 1.15) iv) SS ir-r, 8(r)dr v) M F-F, P 8°(27)di (Hint: 8' () = 8(x)O(y)8(z)) b) Evaluate the integral ſ (1+e") ( )dt...
Q1: Give a bijective proof of the following identity E (%) = 2:1 using the following steps: (a) Use binomial paths represented as sequences (or tuples) of steps to define a set 24 representing the left-hand side. (b) Define a set Nr representing the right-hand side as a certain set of tuples with entries from the set {0,1}. (c) Define a bijective function I : 124 + S2R. (d) Show that your function in (c) is well defined. (There is...
Calculus 1 MAT 201 Final Exam, Spring 1 2019, LAGCC Evaluate the following limits, you may use L'Hospital's rule, if it applies. -V31+4 lim 4-1 -4 a. b. Evaluate the following limit. lim xIn x x-0 2. Evaluate and explain your answer -xsin(x)+cos (x) x+1 130 dx (a.) 130 Differentiate each of the following below using the fundamental theorem of calc part 1 X cos? (1- 51) dt ) g (x) = S_ e (2c) g(t)= J x2t+1 3 Use...
You will integrate the following rational function: -222–162+36 dz (2-3) (x+2)(x-1) -222-162+36 To do this, start by writing (2-3)(2+2)(x-1) A + В. 2+2 + C 2-1 1-3 (a) Put the right-hand side over a common denominator. Enter the numerator of the result. (b) Expand the numerator. It is a quadratic in z, which must equal the numerator of the original function. By equating the coefficients you should be able to formulate linear equation in A, B and C. In each...
For this assignment, you submit answers by question parts Assignment Scoring Your best submission for each question part is used for you O-1 points SCalcET8 7.1.513.XP 7. Evaluate the integral. 1 ydy e5y Jo Need Help? Watch It Tal Read It Save Progress Practice Ano Submit Answer e Assignment Submission For this assignment, you submit answers by question parts. The nu Assignment Scoring Your best submission for each question part is used for your score 0 -1 points SCalcET8 7.1.030...
Part II: Short answer (5 pts. each) Give a short answer to the following questions (1-3 sentences and/or a brief sketch) Make a crude sketch of the world line of a particle initially at rest which then accelerates in the-x direction for a short time, then travels at constant velocity. 1. What is the relation between decay constant and half-life? Prove this relation with a few lines of algebra. If needed, start with the formula mentioned in Essay #1, below....
Consider the following differential equation Note: For each part below you must give your answers in terms of fractions (as appropriate), not decimals (a) The above differential equation has a snaar point at x 0 . It the singular point at x-0 is a regular singular point, then a power series for the solution y(x) can be lound using the Frobenius method. Show that x = 0 is a regular sigar point by calculating: xp(x) = y(x) = Since both...
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