observe that the

Q: What is tl

A: Given function is: f(x) = 3 + cos (3x) We have to find the gradient of the function.

Q: . Find EY.

A:

Q: State the fundamental theorem of calculus.

A: To state: Calculus fundamental theorem

Q: fy at (3,1)

A:

Q: (- 0,a) is measurable.

A: Note that, every interval is measurable.

Q: Use substitution to evaluate dx.

A:

Q: Find fx for f(x, y) = In(x – y).

A: Given that fx,y=lnx-y To find fxx It can be found by fxx=∂2f∂x2     =∂∂x∂f∂x

Q: Show calculations

A:

Q: Suppose Find a.

A: X~B(30,0.21) to find q

Q: Find g that

A: The Probability Mass Function (PMF) is also called a probability function or frequency function…

Q: Differentiate the following with respect

A: Given, f(t)=3cos(2t). Differentiate given function with respect to t.…

Q: Find SU

A: It is given that,         We have to find the side SU

Q: Show that (A\B)\CC A\C.

A:

Q: find dy if y

A:

Q: Assume that

A: Given, X=a, b and  *: X2→X is such that                        x * y * z=z * x * yfor all x, y, z∈X.…

Q: Find the following

A: Given:           ∫ex5+ex12 dx Apply the sum rule: ∫fx±gx dx=∫fx dx±∫gx dx           =∫ex5 dx+∫ex12dx…

Q: et x be

A: Given inequality is: x2≥x Then we get, x2-x≥0⇒xx-1≥0⇒x≥0 ; x-1≥0⇒x≥0  ;  x≥1 Therefore we get, x≥1

Q: We de Notice this.)

A: we will be making use of limits

Q: Compute ∫tan3xsec2xdx.

A:

Q: Iculate the autocorrelation of x, = ej™n/2 + ej™n/3_ ||

A:

Q: | Aut (Z561)| =

A: We have to fin the cardinality of  Aut(Z561) that is  | Aut(Z561)|.   Result used (1)      ϕ(p×q×r)…

Q: Find its ar

A:

Q: A. 1. Show that AAEB ACED

A:

Q: Determine if the following is similar.

A: Two triangles are similar can be find using three ways which are AA (Angle, Angle), SAS (Side,…

Q: This is calculus

A: LHS = ∫-21(x2+x)dx = (x33+x22)-21         = (13+12+83-42)           = 3/2

Q: find fx CX)

A: Let X~P(θ)  We Know the Mean of Poisson distribution is x=θ  Therefore Pmf can be written as…

Q: Evaluate |a sec? rdx

A: Consider given the given integration, Let,

Q: Show tha

A: The given vectors are a=3i-j+4k,  b=i-3j-2k  and  c=4i-3j+2k. This implies that, a b…

Q: =X C R

A:

Q: denote In°(x) dæ

A:

Q: Integrate the following x5 e3x

A:

Q: show that ē ** Jo(bx) dx = %3D 8.

A:

Q: Find dt

A: We have to slove derivative

Q: . What is the PDF fx,(x) of X1?

A: Given that X1,X2, and X3 are iid continuous uniform random variables. Then common pdf is given by…

Q: EER(F}}

A: Introduction - F-test of H0:β1=0consider the hypothesis test H0:β1=0Hα:β1≠0Note that Yi^=b0+b1Xiand…

Q: find the integrating factor

A:

Q: Show E(XY)

A:

Q: Evaluate the following: frsin 3x dx

A:

Q: Find the integrating factor.

A:

Q: as, consider the different

A:

Q: (- 0 ,a) is measurable .

A: Given a statement

Q: f'«) ių faa) = arcsin Ve^

A:

Q: Question 6 Compute )

A: This is the notation used for combinations and the combination is calculated asnCr=nr=n!n-r!   r!

Q: is where mu an mt

A:

Q: Show that

A: (i) To prove that                   22+42-822+3=0

Q: When is lnx negative?

A: Let the function be                                  y=f(x)=ln(x) The domain of the function is all…