Let X and X, independence r.v. have same moment generating function (-) where tsa, let Y=aX+bX, , then My (1) is 1

Q: Find the direction derivative of f(x.y.z)-xy'z at the point p(3,2,1)in the direction towards…

A: To find the directional derivatives

Q: Differentiate f(w) = sinw + w²tan-1w

A: We have to find differentiation of given function.

Q: f(x) = ln[x(x + 6) 5 (x²+2)4] f'(x) =

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Q: Find fyyzz if f(x, y, 2) = cos(3y + az). Then evaluate fygazz at point (, 0, 4). COS

A: *Use chain rule

Q: Can you find the stationary points of V and classify each of them by using the 2nd derivative test?

A: Introduction: A real-valued function defined on a closed or bounded interval can have its absolute…

Q: Q1/ 100 college students were surveyed and asked how many hours a week the spent studying the…

A: Data given   Less than 5 5 to 10 more than 10 Total Male  11 22 16 49 Female 13 24 14 51…

Q: Let f(x) = 6 + V4x – 5. Find f-'(x). f- (x) = for x > 6

A: Given f(x)=6+4x-5 The objective is to find f-1(x).

Q: f(x) = xe (1+e*)

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Q: Detemine whether the differential eguation iš linear of nonlinear and qve reqsons- Ox*dy txdy= Sinx…

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Q: Differentiate the following function: VP - 4V U = u =||

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Q: Assume that f and g are harmonic functions in R^n. Show that div(f ∇g − g∇f ) = 0.

A: Ans- We can start by computing the divergence of the vector field F = f∇g - g∇f:

Q: Prove that the derivativeo P(zx tJ's 4(2Xbjusiy Pirst Princiele 4(2X+)by jusing first Princiele…

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Q: Which interval is f increasing when f' (x) = x³ - x ? (a). (-00, 0) (b). (–1,0) (c). (–1,1) (d). (0,…

A: If f'(x) >0 then f is increasing.

Q: Let f(z) = 4 cos I-3 tan z. %3D S(2) =D %3D

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Q: Let f(x)=V2x/x. Then f"(1)= Select one: 3 16 3 8/2 - 36 7 21 O None of the above

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Q: Jige If f(2) =-3, g(2) =4, f' (2) =2, and g' (2) =, d. then dx -21 16 9. 16 -13 16 29 16 6 jp 3…

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Q: Finel the ralves of a anel b such that the function aV5-x tb-1 it Hax cos(TT Ix) 9 +1+ b(x²-7)…

A: Note: There is an error in question, for the given function a has 2 values but it cannot be possible…

Q: Show Vx Vy[p(x, y) → ¬p(y, x)] E Vx¬p(x, x)

A: Please check the answerin next step

Q: Find and interpret f'( – 2) and f''(– 2). 3 f(x) =

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Q: 3 Let f(x)= x³ - 2x+: Calculate by definition f'(1). X

A: given function to find the derivative

Q: Let f(t) 5t4 - 2t + 6et. Then f'(t) = =

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Q: Suppose f(x) = 6t²√1+tº dt. 1) Evaluate f (2). 2) Evaluate f'(2). 3) Evaluate f"(2).

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Q: Let 7(t) = FindF (t) 구' (t) - <| Question Help: OVideo Submit Question

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Q: Describe the long run behavior of f(x) = x* As x → ∞, f(x) → ? As x → 0, f(x) → ?

A: This question is about function behaviour near infinity

Q: Differentiate the following function: u' = = u = √√ +² +6√√√+³

A: Differentiate both sides with respect to 't'

Q: GrRve the domnin f n(x)= -9-4x|usq iaeoul.ntaton

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Q: Let 11 f(x) = ( – 2a² – 4)(7z² – 4)" - - f'(x) =

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Q: Let f(x)= x³+1. Then (fof)'(1)= O 20 O 36 O 3 O 9

A: Please refer to the image below

Q: Let f(x) = 2 – 2², x > 0 f'(x) = Preview

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Q: Suppose that f(x) = x2 + 17 Find f' (1). f'(1) =|

A: The function fx=exx2+17. We have to calculate the value of f'1.

Q: + Find the maximum value of isu = Sinn Siny Sincnty) U

A: The given problem is to find the maximum value of the given function u=sin(x)sin(y)sin(x+y).

Q: How many people need to attend a party for there to be a > 80% probability that at least two of them…

A: Given information: The probability that at least two of the people share the same birthday is 0.8.

Q: c) Sa* sin*x dx

A: To evaluate : The integral  ∫π43π4 sin4 x dx .

Q: Let f(Wx)= 6x. Then f' (2)= %3D 12/2 1 12 12 24 - 12 6.

A: The given function is: fx=6x

Q: Vリ What is F'(;) 4 ? 16 π 4 π ミ|N

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Q: Let F (x) : tan't dt. Find F' (V3 -1, 4 27

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Q: is ty'+2y=t^2-t+1 a linear ODE in standard form?

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Q: A group consists of 5 Democrats and 8 Republicans. 7 people are selected to attend a conference. a.…

A: In the given group there are 5 Democrats and 8 Republicans.