Prove that −(−v) =v

Q: Let X and Y be independent, and let X be N(10, 1) and Y be N(11, 1). PIX >Y),

A: From the given information, X and Y are independent random variables. Let X be a N(10, 1) variable…

Q: A fair coin is tossed two times independently. Let H₁ = {1₁ (1, if head is obtained at the ith toss…

A: When head is obtained at 1st toss then H1= 1  When head is not obtained at 1st toss then  H1= 0 When…

Q: Compute divF and curlF for F = -r°(y – 2)i – (2² + y^)j+()k. 422

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Q: Let u = (-3, 1) and v = (0,3). Compute the following: u.v= • = | | i|| 2 = −1 (u · v) • (−1ū) · v ū⋅…

A: Step 1:Step 2: Dot Product (·):The dot product measures how much two vectors are aligned with each…

Q: Let f(x1, x2, X3)=( x1³ + x2, x1² + x3). Find df(1,2,3)(-3, –2, –1).

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Q: Prove that xJ(x) = vJ , (x)– x (x) X V. v+1

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Q: re 1 da Ji rVI- (In x)²

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Q: Find the Re and Im parts of exp(z?)

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Q: Find | |- •√√√√ V 5x ry sin(x² + y2) dedy

A: ∫02π3∫05π3xysinx2+y2dxdy

Q: Use the IVT to show that f (x) = x3 + x takes on the value 9 for some x in [1, 2].

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Q: 2 16 v2 6. Prove that x V(2 – x) dr = 15

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Q: 2-2x find (fif) G) to use f Cx) = x

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Q: 2.11) Write as 1 y- linear combination of X₁² -2 2 F 2 -1

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Q: Prove or disprove: If (xn) and (yn) are subsequences of each other, then xn = yn.

A: Definition: Suppose ann∈ℕ be a sequence. A subsequence of this sequence is a sequence of the form…

Q: IF| = r r) = -i = 5xi + 2yj – 2zk so be it where div() , grad(f find all of

A: Solution:

Q: Let x and y be positive reals such that 3 3 x³² + y² + (x + y)³ +30xy 3 = 2000. Show x + y = 10.

A: x3+y3+x+y3+30xy=2000 We have to show x+y=10

Q: U(9) has how many elements?

A: We know that- U(n) is the set of natural numbers  that are less than n and coprime to n.

Q: Let 1 3 A = -2 -1 and В - 2 -2. a. Find AT and show that (A")' = A. b. Show that (A+B)" = AT + B".…

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Q: 4 x² + 4

A: Follow the procedure given below.

Q: Find f(-5e3* + VE)dt

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Q: Q-12)-for the model below Max z=10X1+5X2 st 4X1+2X2540 3X1+3X25 30 X12 0, X2 20 MAX Z=- O 75 O 100…

A: Linear programming. Graphical method

Q: Eualuate the function hx)= X +Sx2+3 at the given and Simplify Values of the indePendent variable…

A: The given function is :hx=x4+5x2+3we need to find h3a

Q: Show that al/bc, c to gives a/b ?

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Q: E Show that x'+ 3x+ 2 has 4 zerosin Ze

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Q: If f(x) =x* + 3x² – x – 15, then f" (-2) would be A. -48 В. -24 С. 24 D. 48

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