i Show that d dx(e 4x 4 xe 4x ) pxe 4x , where p is an integer to be found ii Hence find the exact value of 0 ln2 xe 4x dx, giving your answer in the form a ln 2 b c, where a, b and c are integers to be found ...

i To find ddxe4x4 xe4x we can use the product rule of diffe ...

i. Show that d/dx(e 4x /4 xe 4x ) = pxe 4x , where p is

Question:

i. Show that d/dx(e^4x/4 – xe^4x) = pxe^4x, where p is an integer to be found.

ii. Hence find the exact value of ʃ₀^ln2 xe^4x dx, giving your answer in the form a ln 2 + b/c, where a, b and c are integers to be found.

Fantastic news! We've Found the answer you've been seeking!

Step by Step Answer:

Related Book For book-img-for-question

Cambridge IGCSE And O Level Additional Mathematics Coursebook

ISBN: 9781108411660

2nd Edition

Authors: Sue Pemberton

See More Books

Question Posted: Sep 06, 2021 01:20 AM

See More Questions

Find the exact value of each expression. a. b. c. d. -14 sin sin sin(sn(-3) sin sin cos (cos (-45))
Find the exact value of each expression. 35. (a) log: 64 (b) log, (b) In e 36. (a) logs2 37. (a) logo 1.25 + logio 80 (b) logs 10 + logs 20 3 logs 2 38. (a) 20g:3+log: 5) (b) e3a2
Find the exact value of each expression. 63. (a) sin-(3/2) (b) cos-(-1) (b) csc- 2 64. (a) arctan(-1) (b) aresin(-1//2) 65. (a) tan-3 66. (a) sec-2 (b) arcsin 1 (b) tan 67. (a) sin(sin-0.7) tan - (b)...
(a) Employing the intercept technique, determine the average grain size for the steel specimen whose microstructure is shown in Figure (a); use at least seven straight-line segments. (b) Estimate the...
Give the name and formula of the acid corresponding to each of the following oxoanions. a. Selenite ion, SeO32 b. Sulfite ion, SO32 c. hypoiodite ion, IO d. nitrite ion, NO2
Zimmermans Bank is the only bank in the small town of St. Thomas. On a typical Friday, an average of 10 customers per hour arrives at the bank to transact business. There is one teller at the bank,...
Suppose that you purchase the forklift for $20,000 by borrowing the purchase price using a four-year annuity loan. What would the monthly loan payment be in a perfect capital market where the...
Davenport Construction Associates compares actual results with a flexible budget. The standard direct labor rates used in the flexible budget are established each year at the time the annual plan is...
Suppose we have a nMOSCAP made of Si. Suppose the channel doping is too strong at p = 1019 cm-3. All plots should assume the metal is on the left side. For this problem, we apply Vgs = Vth. (a) Plot...
Fire Loss, computing inventory costs a distraught employee, Fang W. Arson, put a torch to a manufacturing plant on a blustery February 26. The resulting blaze destroyed the plant and its contents....
a. Given that y = (x + 8)x 4, show that dy/dx = kx/x 4, and state the value of k. b. Hence find x/x 4 dx.
The point (/2, 5) lies on the curve for which dy/dx = 4 sin(2x /2). a. Find the equation of the curve. b. Find the equation of the normal to the curve at the point where x = /3.
In a continuous manufacturing process, chlorodifluoromethane (CHClF 2 ) initially at 10 bar and 420 K, passes through an adiabatic pressure reducing valve so that its pressure is 0.1 bar (this last...
Patrice recently returned to Australia after working in Singapore for seven years. On 1 January she gained her Australian tax residency. Her retirement savings accumulated in a Singaporean fund at...
A projectile is launched horizontally with a speed of 25.2 m/s. If the projectile takes 2.63 seconds to reach the ground, how far above the ground was the launch point?
Company ABC expects to earn 13% on reinvested earnings. If the company pays 30% of its earnings as dividends, what will be the stock's dividend growth rate?
Find f(g(x)) and g(f(x)) and determine whether the pair of functions f and g are inverses of each other. f(x)=x-6 and g(x)=x5+6 f(g(x)) = x g(f(x)) =
Write a Java function that efficiently computes the nth Fibonacci number using dynamic programming.
Given the functions 2x and |x|, show that (a) These two vectors are linearly independent in C[- 1, 1]. (b) The vectors are linearly dependent in C[0, 1].
Fill in each blank so that the resulting statement is true. A solution to a system of linear equations in two variables is an ordered pair that__________ .
Danielle Anderson, your client and a cash method taxpayer, works full-time at a music store located in a mall. She assists the manager in buying decisions, serves customers on the sales floor, and...
Peter Baumann, your client, wants to sell a printing press to Chamberlain Corporation for $50,000. Pete has used the press in his business for two years and its adjusted basis is $90,000. The Coxmann...
John and Kathy Brown have just been audited and the IRS agent disallowed the business loss they claimed in 2015. The agent asserted that the activity was a hobby, not a business. John and Kathy live...
3. Use the following information for the following questions: ABC Mutual Fund's total return (geometric mean over the past 5 years: 10.25% Risk Free Rate has averaged 2.5% Beta of the company's...
How much would a $6,750 investment yield after 65 years at an annual rate of return of 6%?
A swiss stock has a monthly risk of 0.02 and the CFH/$ exchange rate has a monthly risk of 0.07. The correlation of these two risks is 0.21. What is the annual risk of a US investment into this stock?

i. Show that d/dx(e 4x /4 xe 4x ) = pxe 4x , where p is

Question:

Step by Step Answer:

i To find ddxe4x4 xe4x we can use the product rule of diffe...View the full answer

Cambridge IGCSE And O Level Additional Mathematics Coursebook

Students also viewed these Business questions