d 11. If{(x¹ - α₁x¹-¹ + A₂xn−²_ dx 0 ≤r≤n, is equal to (A) ¹²!! r! (n-r)! r! n! (n-r)! (n-r)! (D) n! (E) None of the above <<-... + (-1)"an)ex} = x^ex, then the value of ar,

Q: 13. (a) Find a number 8 such that if x- 2 < 8, then 4x - 8 < 8ɛ, where ɛ = 0.1. (b) Repeat part (a)…

A:

Q: 7. lim X-2 x+2 A. 1/4 В. 1/-4 C. -4 D. DNE

A: We can find the answer as below.

Q: り If X~メ (2)、 Find the 32-moment of x about zero

A: Introduction: The random variable X has a chi-squared distribution with 2 degrees of freedom, that…

Q: If X~N(3,16) then P(4SX<8) = 0.5987 0.2957 0.8944

A:

Q: 6x2 1 + x + x² + x3 6x + 4x +2 6x2 + 4x + 2 xp. 1+x+x + X xp. .2 In[4]x² +x + 1|]+ Inx. O A. 2In(x³…

A: Consider the integral  ∫016x2+4x+21+x+x2+x3dx∫6x2+4x+21+x+x2+x3dx

Q: Find f(x) iff, (p) Hence deduce F .

A:

Q: (B) 3 (C)2 If D* f (x) = 2f (x) D(f (x)), then (D*(x/nx)), is- (A) 4 BYA 16

A:

Q: 27. Which of the following is equal to -2? dx (a) 2* (b) (In 2)2* (c) х2*-1 (d) In 2

A:

Q: 15. Suppose X - Bino(2,). Find P(X = 0|X < 1). (а) 3/4 (b) 1/4 (c) 1/2 (d) 1/3 (е) 2/3

A:

Q: 2) S(n)-10-2 at n 5

A: Given ,  f(n) = 10 (2)n     ......... (1) We have to find the value at n = 5 Put ,  n = 5 in…

Q: 3. 2y"" − 3y" – 3y² + 2y = (e*+ex)²

A:

Q: 7. [(In x)² dx

A: Given- ∫(lnx)2dx We have to evaluate the given integral. Here we will use the following formulas- ∫u…

Q: 7) Find f(x) if f(x) = (103x + 2)2. a) 6 In 10 10x + 4 b) 6. 106x 105x + 3 c) (6x + ○ 4) 4) 106x d)…

A: Topic:- application of derivatives

Q: If f(3) 9 and f'(x) ≥ 2 for 3≤ x ≤ 8, how small can f(8) possibly be? f(8) ≥

A:

Q: of n if each function had to ensure that the error of the method is 0.0005 find the approximate…

A: We will use formula for trapizoidal rule and its error

Q: 7. Show that Sx" Inx dx =Inx-+ c. n+1 %3D + C. n+1 n+1]

A: Using integration by parts we can prove the given integral.

Q: 3) Using Quotient Rule ()'=€'gfg),find (±)' = (3×/eX)' = A) (3/e)X[In3-1] B) (3/e)x-1 C) 3×ln3/eX D)…

A: Topic:- derivatives

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

A: We know that ln(1-x)=-x-x22-x33-x44-...=-∑n=1∞xnn     ...(1) on the interval (-1, 1)

Q: 2. Solve f e** using Simpson's 1/3 Rule with n = 8.

A: The Simpson's 13rule is given below by,  ∫abfxdx=h3fx0+4∑i=1, i is oddn-1fxi+2∑i=2, i is…

Q: x²-3x + 7 (x² - 4x + 6)² dx

A:

Q: (In be*) dx b = constant A. x + In be* В. 1 С.b D. 1+ x

A:

Q: If 40 f(x) dx = 13, then compute the value of the following definite integral. 20 8 fºr(² f(5x) + 4…

A: By the answering guidelines of Bartleby, we can answer only first question from multiple questions,…

Q: Compute *In (9)/5 Jo e5x (e5x + 8)5 dx.

A:

Q: ! Given f (x) = {x + 2 if x > 10 lx – 7 if x < 10' D. ! determine each of the following. a.) f(14)…

A:

Q: 6. In which of the following intervals is the function y = x + 3x2 increasing only? -3<x<-2 -3<x<0…

A:

Q: 107. Find a bound for the error |M16 x'dx

A:

Q: 17. lim (Vn² +n – /n? +1) = } n00

A: To show: limn→∞ n2+n-n2+1=12

Q: 6. 22x+x dx

A:

Q: 9. Given that 00 2n+3 f x) - Σ(-1)" (2n +1)! n=0 Find f '(0)

A:

Q: Find 29x(6)'-1dx

A:

Q: 5) f(x) =x' - T <x<TI Ans. Odd

A:

Q: - Expand f(x) = ;-X<XLO ~) = { ² }); ; OLXLX in F.S.

A:

Q: 12. Ext(X\Ext(A))= * , Ext(X\A) O Ext(A) O X\Ext(A) O XIA

A:

Q: 2) f(n)=10 - 2" at n= 5

A:

Q: nf'(x) =

A: