9. In(1 – x²) = -) on the interval (-1, 1) n=1

Q: 1/2x (In2) In x (use L'hopital's Rule)

A:

Q: 2. the rate at which the total average number of COVID cases is increasing at x = 10 tents and= 1…

A: The solution for question no 2 is given below:

Q: السؤال 2 when hv hvo Electron is ejected from surface of metal ylgn O

A: Since we know that​ The ejected electrons have a distribution from 0 to  hv-hv0

Q: (2) Use a proof by ca. If is int er

A:

Q: If n = 18, then the interval of the form (- t(n-1), alpha/2 , t(n-1), alpha/2), that contains 99% of…

A: From the given information, number of observations n = 18. Confidence level  Level of significance

Q: Use the Golden Section Search to find max-x2 – 1 s.t.-1<x<0.75 with the final interval of…

A:

Q: 5. Show that Beta(a,b) belongs to the 2-parameter exponential family

A:

Q: a random varrable Y has a cumdative df fy if 04 >4 probability hat Y falls between 2land 3 find thd

A:

Q: @) 2) Fs of (x) = -PFC (Psy) -} [ If f (x,y) → as 6004X proof. (H-w.) then в

A: Introduction: The Fourier sine and cosine transforms are variations of the Fourier rework that do…

Q: Assume that after w months,butterfiles populace in 1000 is calculated as F(w)=12w+cos(16w)+n×100…

A: Minimum and maximum of a function depends upon all the variables present in the function.

Q: de -- e* + 4e* -00

A: Given

Q: A certain young lady decides on her twenty fifth birth day that it is tir weights 100 Kg. She has…

A:

Q: Suppose that we observe that X1, X2, . . . , Xn  are iid∼ U(0, 1). Show that X(1) converges in…

A: A sequence of random variables Xn is said to converge in probability, denoted as Xn→pX, if…

Q: 7 Evaluate the improper integral, if exists : dz (5 - 2)3

A:

Q: 1. Show that cosh 4x = 8cosh“x - 8cosh? x + 1 .

A: Given problem:- Show that cosh(4x) = 8cosh4x - 8cosh2x + 1

Q: 2. Show that X H→ In x is increasing on (0,0) and that In 1 = 0:

A:

Q: 2) Determine the interval and radius of convergence of 2 '(x+5)** (2n +1)! 34n-1 n=0

A:

Q: There is one male baby seal for every nine female baby seals. Let X be the number of male baby seals…

A: Let p=P(male baby seal) = 1/9 Here n=5 Note that X follows a Binomial distribution with n=5 and…

Q: Number 5

A: Square both sides and then simplify Use (a+b)^2= a^2+2ab+b^2

Q: 59. Show that 1- sin x dx converges. x? 00

A:

Q: Compute the following integral: / secʻ(5x) tan" (5x) de 1 (tan(5x))*+3 + C 1 а) 5R + 5 (tan(5x))*+1…

A: We can solve this by using some basic concept of integration as substitution method .

Q: 1. find the de rivative 3 Inx

A:

Q: Use the linear approximation to estimate In (√0.99).

A:

Q: The radius of convergence (2n + 3)! (x- 1)" is | None of these infinity

A: Given ∑n=0∞(2n+3)! (x-1)n Compare it with ∑n=0∞ an(x-x0)n Then an = (2n+3)!an+1 = (2(n+1)+3)! =…

Q: 23. -(-Cnd)→e -evd dz

A:

Q: 2. Rainwater accumulates in the ditch as follows: 10 centimeters of water in the 1st second, 15…

A:

Q: Find the derivative of 4 ^ (3x) * O 12x O In 4 O x In 64 O (4^(3x)) In 64

A: We can solve this question taking derivative of both side wrt x

Q: - show that Ž Lad" n2 Conver Jeat IS n=3 divergen't from integrall Test. or Use

A:

Q: 1. Express into parital fraction. Hence evaluate y2 -4 *2-4

A: according to our guidelines we can answer only three subparts, or question and rest can be…

Q: Find lower bound for f(n) = 5n².

A: To find the lower bound for f(n) = 5n2

Q: Find the radius of convergence for: 3 (n!) ³ (3n)! n=1 xn

A: Recall that the radius of convergence for a series ∑n=1∞anxn is R=limn→∞anan+1

Q: 8= From Orelinay Differeulial eguaton of following by Eliminaking the y==x(aCos 2x + bSin2x)

A:

Q: None of These cosh(4t) 7. 2. 7. - sinh( 21) sinh(4t) 7. cosh(21) 7. Sて 1/2 1/2 1/2 1/2

A:

Q: If In x + In(x - 7) = ln(7x), then x =

A:

Q: 1. What should be A for the path independent of (2,4) xy + A 2Ay – x + xp- y? fip- (1,2) Moreover…

A: According to the given information, it is required to find the value of  so that the below integral…

Q: 8. Use the integral test to determine if IM8 k² (k³ + 2)3/2 converges.

A:

Q: The average number of customers at a windów of a certain bank per minute during banking hours is…

A:

Q: 4. Letf(x)=x22/5 - 19x². Determine the largest n for which fis n-times continuously differentiable.

A:

Q: 1.Find the interval and radius of conv. of In(1 - x2) ?

A: Maclurin series representation for ln(1- x2 ) is  ∑n=0∞-(x)2n +2n+1   (Why?) Explanation As ln(1+x)…

Q: 5. Show that cos .3 G) do not converge.

A: We need to prove that: cosnπ3 does not converge This can be proved as follows:

Q: 2End 2 povel seies expressan for the funchon flx) =dan'(sn) Whal o As interval or convergencl

A:

Q: Evaluate the improper intergal 1 -00 dx using the residue (x² + 16)3 theorem. 00 2

A:

Q: 8. The improper integral | 1. x²+2x+5 1.

A:

Q: Choose the most appropriate answer: Evaluate the integral : S(19 Inx) dt O 38(2 ln 2 + 1) o 19(2 ln…

A: The integral is ∫12(19 ln x)dx

Q: 3-Expand In [x? sin³ x /vx2 +1]

A:

Q: Evaluate 1-(In x) x In x -dx

A: