Match the following functions with their recursive definitions. > n! n(n+1)(2n+1) 6 2n n² 1. f(0) = 1, f(n) = n × f(n − 1) - 2. f(1) = 1, f(n) = f(n − 1) + 2n – 1 3. f(0) = 1, f(n) = 2 × f(n − 1) - 4. f(1) = 1, f(n) = f(n-1) + n²

Q: Let X x b(n,-) and E(3x) = E(3-5.x) find n.

A: Given X ~ B(n, 12) P(X=x)=Cxn px (1-p)n-x; x=0,1,....n…

Q: If f(1) =x² – 9 and g(x) = then (go f)(ī1) is I+8 O 16.00 O 0.20 O 64.00 0.80 O 7.00

A: Function

Q: Find [4x³ (In x)² dx. O A. 1.4 X x In²x + In x + O B. x² ln² x - ln x + O C. x ln x O D. x ln x X 2…

A: Note : according to our gauideline, i can solve oy first so please reroute the remaining question.…

Q: Which of the following is correct for F (۲) ce (1) 0 s+) cety (1) - (۱)

A: We have to find the correct choice.

Q: 2 nd the domain of the function f(x) : (x² – x – 12)(x2 + 1)

A:

Q: If f(n + 1) = f (n) + 5 and f (1) = 100, what is f(4)?

A:

Q: Find the domain of the function f(x) I - 8

A: Domain: It is the values of input x that can be given to the function so that function will be a…

Q: (b) Find the big O of the function f(n) = n²" + n"

A:

Q: 2. Suppose that f(x) = ((.x² + x·5).5 +.r.5).5 when x ≥ 0. Find df(x)/dx. •5 (@ï¥2³ )² +x²)+…

A: The answer is given in step 2

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A: Solve the remaining three

Q: Suppose that the mice population in a certain town follows the formula p(t) = 3000t2 where t > 0 is…

A: We have to tends t to infinity.

Q: The function f(n) = 1.5n+√√n is (n). O True O False

A:

Q: If f(1) = 4 and f(n) = f(n – 1) + 3 then find the value of f (4).

A: Given f(1)=4, f(n)=f(n-1)+3

Q: 3- 5x – 3 < 1.

A: Given : 3-|5x-3|&lt;=1.

Q: For items 1 - 2. Let f (x) = 3x² + 9x – 3 and g (x) = 4x³ – x² + 4x – 9 %3D 1. Determine (f – 9) x.…

A: We know, f+g x = f(x) + g(x) f-g x = f(x) - g(x) fg x = f(x) g(x)

Q: P(x) = 5 x + 13 x5 − 7 x6 − 2 x2     If P is written in descending order, what would be the final…

A: given polynomial is                                               P(x)=5x+13x5-7x6-2x2 P is written…

Q: c. x[n] = e and d[n-5]

A: As per the question we have two discrete signals : e-n² and  δ[n-5] And we have to find the…

Q: Given f (x) = k(x – 1)2 + 1, find a simplified expression for k, in respect to a, if f-1(16a*) =…

A: Topic = Function Finding the Inverse of a Function:- First, replace f(x) with y. Replace every x…

Q: The function j(x) is a sum function of f(x) ands g(x). If f(x)=x2+4x+4 and g(x)=x2+(k-16)x+k,…

A: Given: f(x)=x2+4x+4 g(x)=x2+(k-16)x+k j(x) is a sum function of f(x) and g(x) j(1)=0

Q: #8: Suppose that an = as 8n a₁²2² +2a₂x³ + 3a3x²4 + 4a4x³ + ... (i) Σf(n)x"+2 n=0 (ii) g(n)x+1 We…

A: This is a good exercise in summation and we shall see how to change the indices.

Q: Determine the recursive definition for the function f(n) = n + 2", where n ≥ 0.

A: Determine the recursive definition for the function f(n) = n + 2 , where n≥ 0.

Q: Suppose that the functions s and t are defined for all real numbers x as follows. s(x)=3x-2 t(x)=x-4…

A: The function s and t are defined as  sx=3x-2 tx=x-4

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A: Radians in an angle of - 670°  =   ? We know,      180o = π radian

Q: A utility function is given as                         S (n) = - (n – 4)2 + 15             where S…

A: Given function

Q: x - 6 for x 0 Find f(0)

A: Since, from the given conditions, we have following values of function f(x):-When value of x is less…

Q: Suppose f and g are two functions with nonnegative values. If f(n) is (n) and g(n) is (n³/2), then…

A: We have given that , f and g are two functions with non - negative values. If fn is θn. Also , gn is…

Q: L. nft 7r 2x+1 1 4) f(x) = 2 I- 3 < 1 f(1)= f(-2)= f(6)=

A: The given expression is:

Q: (a) Show that for n> 1 we have F2 = FnFn+1 − FnFn-1. (b) Use part (a) to show that F² + F² + . + F²…

A: Fn denote the Fibonacci sequence, satisfies Fn+1=Fn+Fn-1.              n≥2 And         F1=0,…

Q: For the model (1-B)(1-0.2B)X(1-0.5B)a,, find forecasts for one and two steps ahead, nd show that a…

A: Given: Let Xt∧k=1.2 Xt∧k-1-0.2X∧tk-2 ---(1)

Q: Which of the following statements is not true for f(x)? S2+3 x 0 f(x) = o f(1) = 4 o f(0) = 3 %3D…

A:

Q: 2x+ 1 Let f(x) = Compute f (2). 3x - 2 O A. 0 O B. -2 OC. 1 O D. 1 3 O E. 2 3.

A: Just I have used the quotient rule of derivative and easily find the required solution. Option (B)…

Q: 12x iet f (x) = 2x-17 for x 10 a. Find f(4)=_ b. Find f(24)=.

A: The probability density function is fx=12x-17 , for x&lt;106x+2 , for x≥10.