(a) Suppose z1, z2 € C and z satisfies the conditions Re(2) > 0 and Im(2) = 0. Show %3D then that Ln(z12) = Ln(z1) + Ln(22). (b) Consider following statement: Ln(-1+ i)" = n Ln(-1+i) holds for all n e N. Determine now whether the statement is true or not, by either proving it for all neN, or by exposing a value for n EN for which it is not true.

Q: If E (X) = 1 and Var (X) = 4 then E (X² + 2X – 1) = :- 1)

A:

Q: Let T(x) and T(y) be the complete future lifetimes for the lives x and yrespectively. If T(x) and…

A: Given: The whole future lifetimes for the lives x and y, respectively, are functionsT(x) and…

Q: Suppose f= f(x) satisfies f(1) = 7 and f(1.002) 7.008. Estimate the value of at x = 1. dt %3D

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Q: dx J x. In5 (x)

A: Given that: ∫dxx·ln5x…

Q: ii) 2 log, (x)– log2 (3x – 4) = log, (x – 1) – 1

A: We make the coefficient 2, exponent inside the log.  And for 1 we replace it by log22 because…

Q: Show that E(X-µ)³ = E(x³) −3 [E (x²) ][E(X)] + 2[E(X)]³

A: The linearity of expectation property: With the assumption that, Xi's (i=1,2,...n) with n positive…

Q: Find f"(x) for the functions x² +5x f(x) = ex b. f(x) = (x² – 1)e* a.

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Q: If g(x) = max {x, 1/x} what is g(x) when x ϵ N2 (.5)?

A:

Q: If f(x) = (2x – 1)(4x + 5), then a. f( – 1) = b. f'(– 1) = | c. f''(– 1) =

A: Since we only answer up to 3 sub-parts, we’ll answer the first 3. Please resubmit the question and…

Q: By using Rodrigue's formula, prove the following relation Ph+1(x) – Ph-1(x) = (2n + 1) P,(x) 4- %3D

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Q: If f(x) = an(x – 1)²n for all æ, then f'(3) is equal to n=0 OA. 2nan-122n-1 n=1 В. 2 2na,22n n=1 OC.…

A: According to the problem, we have

Q: Given function G(x)= 3√2t² - 2 dt. Which V one of the following is true? A) G(3) <G'(3) <G"(3) B)…

A:

Q: b. 8(x) = E ()" k = 1

A: domain: where function is defined

Q: After being closed for approximately 18 months due to a pandemic, Disneyland re-opened to California…

A: Given that                                         N(t)=∫0tE(t)-L(t)dt where E(t) is rate at which…

Q: If f(x) = (2x – 5)(3x + 5), then - a. f(1) = b. f'(1) = %3D

A: Solution -  Given function is as -  f(x) = (2x-5)(3x+5)we can expand it further - f(x) =…

Q: 2. The equation of the horizontal asymptote of the exponential function f(x)=7(0.5*4)–-1 is: A) y =…

A: The equation of the horizontal asymptotes of exponential equation f(x)= 7(0.5x-4)-1

Q: a) Given a surjective function f : [-1, 1] → [-1, 1], prove or disprove: f-l (f{0}) = {0}. b) Find…

A:

Q: 5. Let X1, X2, .. be iid Exponential (0), and Y1, Y2,....be iid Expomential (20), = min {n :I (X, >…

A: Given X1, X2, .... be iid Exponentialθ, and Y1, Y2, .... be iid Exponential2θ and X's and Y's are…

Q: AR.7.38 Find f(x) and g(x) such that h(x) = (f o g)(x). h(x) = (1 – 5x)? Suppose that g(x)% = 1-5x.…

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Q: Which of these functions have a domain of (-*, 0)? Select all that apply. A f(x)= e*+2 B g(x)=…

A: We will find such Fucntions.

Q: 3. The Chain Rule. Solve Dx (2x2 + 2)* V2x CSC X

A: This is a problem of differentiation of the function. Based on below formula we will calculate the…

Q: If ln x + ln(x − 3) = ln(7x), then z

A:

Q: Suppose f(z) = In z and g(z) = ecos. Let h(x) = f(f(q(=))). (a) Find a simplified formula for h(z)…

A: Solution of given question is followed by:

Q: (ミ) (20) %D %3D

A: Given R(z) = 2z2+2S(z) = 3z Then (R∘R)(z) = R(R(z))= R(2z2+2)= 2(2z2+2)2+2 = 24z4+4+8z2+2=…

Q: If g(t) = 2r +9t2-7 find. %3D g(0) = -7 g'(0) = -7 g" (0) = g"(0) = %3D g(4) (0) = g(5)(0) =

A:

Q: Suppose P(t) represents the population of a certain mosquito colony, wheret is measured in days. The…

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Q: Find ds ldx if y=3) X(X+1)(x-2) (x² +1) (2x+3)

A: Note:-Since you asked multiple questions, according to our policy we can answer only first question…

Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.