Let o € C (RN), heR - {0}. For teR', we set 0(r +th) – 6(x) (1) = t. 1- Show that o e C (R^).

Q: c. - f'(1) = (3e³ – 2p¹³) In (5p¯² — *√p) -

A: To differentiate the given expression f′(1)=3e3−2p−1/3ln(5p−2−p−1/4), we'll need to apply the chain…

Q: 10) Show that [x] = −[−x] A 11) suppose that g: A → B and f: BC, where A = B = C = {1,2,3,4}, g =…

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Q: draw the plot for the signal vs time for  f(t)=5e^−2t,for −1<t<2 zero otherwise over the domain…

A: In this question, we need to plot the graph of the given function f(t).

Q: ex: show that (H.W) (xJ,(x)' = -x Jv+1

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Q: The Domain of ƒ(x) = V1- x is

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Q: 5.16] Use the function f (x) = xe¯ ¯x² to find fave on [0,4] %3D

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Q: Let 7(t) = Find (t) 7' (t) =

A: Given query is to find the derivau of r(t).

Q: The number of representatives of a political party, N, in a city council depends on the percentage…

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Q: X1, ., Xn are idd. find the MLE and cramer rao lower bound for unbiased estimator for theta. f (x |…

A: Given  fxθ=θ              when x=-11-θ2θx     for x=0, 1, 2, ....

Q: Suppose f(x, y, z) = xyz + 2xy + 2² · Compute the following values -(2,8₁16) - (-2,-8, 16) (1,-1,0)…

A: We have to find functional value.

Q: 7) Use Theorem 7.1.1 (Table) to find L{f(1}} for the following: S)-(e*-e*)}° a.

A: The given function is f(t)=(e-3t-e5t)2. Expand the function implies, f(t)=e-6t+e10t-2e2t The Laplace…

Q: dx Suppose 10 = x + y' and both y = f(x) and x = g(t). If = 2 when x = 1 and y = 3, %3D dy when x =1…

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Q: 2 -JM 3 0 5 Determine whether v is in the range of T. Fully justify your answer. 1 -2 -1 Let A = =…

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Q: -2 Suppose f(x) = f(x) dx Evaluate: A - In (2) B - 4 3 16 D In (2)

A: Solution... Answer is.  Option..(B)

Q: Evaluate SIL. dydzdke, where E = {(x,y,z): (2+z12<x< 2, - (4 - z)2sy <(4 -2)12, 3<z 58}.

A: Given: The given integral is ∫∫∫Rdydzdx The given intervals are (y2+x2)12≤x≤2, -(4-z2)12≤y≤(4-z2)12,…

Q: let it be 2= f(x,y) and Y=tan' () and X = === In (r²+5²) Prove that fxx+fxy= (y² + S) (fr+fso)

A: We have to prove

Q: Q3. Find y= fx) such that y

A:

Q: Differentiate the function L(k) = cosh¯' (/T+ k² ). O (k² + 1)-1/2 O 1+ k2 1+k

A: ddkcosh-11+k2

Q: 4. Find f"(2). (a) f(u) = 2u²5 – u).

A:

Q: Show that Var (Y) = Var(ε₁) = 0².

A: Let us consider a simple linear regression. The equation of a simple linear regression model is:…

Q: If X~BET(1,2) then E(X)= (1 2/B (1/B

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Q: let foo- X-1 when x+i- Féndavalde of fethat calil makefis continueus at xe

A: For a function f(x) to be continuous at x = a the condition is:

Q: Oind Let g(2) = u(2)+iv(2) be ol complete function hiC →C, h(2) = e¯( v(a)+iu(2). Show that if h is…

A: gz=uz+ivz is a complete function and h:ℂ→ℂ by hz=e-ziuz+vz is a entire functionTo prove: g is a…

Q: 7. Ax)= 2x' -5

A: We have to find

Q: . There is a function f that's continuous at 0 and f(x) = f(2x) for all x's please show that f must…

A: Answer for sub question 1a: First step is to show fx=f2-nx for each integer n≥0. If n=0: fx=f2-0x…

Q: Let {X} be i.i.d. such that X₁~ Pa(4, 1500) and suppose that N(2) ~ Po(100). Find E[S(4)] and…

A: Given that  be iid. such that  and

Q: 3. If f(x)= kx³ -1 and f¹(15) = 2, find k

A:

Q: Suppose that P(A') = 0.3, P(B) = 0.8, P(A U B) = 0.9. Find P(A), P(An B), P(An B') and P(A'|B).

A: We have given that P(B) = 0.8 We have to find P(A),  and

Q: If you are asked to find L4 for f(x) = edz) + In(x) on the interval [2,10], what would the value of…

A: From the given problem:   fx=e3x2+lnxa,b⇒2,10   As we know that the expression for the step size is:…

Q: 1 (d) Last week, Amy walked a median of 7.5 kilometres each day. 1 kilometre = 0.6 miles The table…

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Q: Define h as x 2 Determine whether the function h is continuous h(x) = {3, x2 or discontinuous at x…

A: NOTE: Refresh your page if you can't see any equations. . if the function h(x) is continuous at x=2…

Q: 7. Modify B(3) to construct a C* function C(2) which satisfies C(2) = 0 if z S 0.. a. b. C(z) = 1 if…

A: please see the next step for solution

Q: =Xtanx dk, Prove that ="IH (n+1)I,+(n-1) -1 T 1 2 n

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Q: Exercise 4.1.5. Which of the following formulas define functions R → R? (2) p(x) = (x^(2)+3) / (x+5)…

A: