Suppose that f : A → B is a function, C C A and DC B. (a) If f is surjective, prove that D = = 3[f{D].

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A: A statistical distribution is called probability distribution if it satisfies following: (i) All…

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Q: K H L Consider the graph given above. Give an Euler trail through the graph by listing the vertices…

A: Euler trail If there exists a trail in the connected graph that contains all the edges of the graph,…

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Q: 40-45 Special Function Values. Find the values of 40. sin (3 + 4 Ti)

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Q: Calculate 1₁ ₁² ² a feas = e¯² ds for the piece of the cylinder x² + y² = 16 for 0 ≤ z ≤ 7.

A: we have to find the ∬Se-zdS for the piece of the cylinder x2+y2=16 for 0≤z≤7

Q: 3. Let a₁ = 2, a2 = 1, and for each natural number n > 2, let an 2an-1-an-2. Prove that for all…

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Q: How many different initials can someone have if a per son has at least two, but no more than five,…

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Q: 5. Prove that every graph of order 6 with chromatic number 3 has at most 12 eges.

A: Solution :- As per guidelines.i solve 5th number.

Q: Q3. Find the solution ylt) of the initial value problem (1) Hat =0, l0\ = | Where ə is o postve…

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Q: Find the matrix of the quadratic form. Assume x is in R°. 5x - 4x3 + 3x3 + 18x,x2 - 4x,×3 b. 3x -…

A: We want to find matrix of given quadratic form.

Q: 1 |Leax sin(bx)] eax [a sin(bx) – b cos(bx)]+ C * Using the formula dx = ах a² + b². Sie [e-8x…

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Q: 4. Let R be the relation xRy if 3| (x – y) on Z. Prove that R is an equivalence relation.

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Q: Use the RSA cipher with public key (n, e) = (713, 43) to encrypt the word "TEE." Start by encoding…

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A: Solution :-

Q: Evaluate the definite integral. Son f (x) dæ, ƒ (x) =6e" /(4+e*)

A: It is known that: ddxekx=kekx∫ekxdx=1kekx+C

Q: Clairaut's Theorem Let DCR be a disk containing the origin and assume that g : D R is a function…

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Q: Determine which parametrization describes the circle depicted in the following plot: t = 1.8326 21…

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Q: Quiz 1 1.maclaurin series cos hx

A: Given function is f(x) = cosh(x)

Q: rb+c f (x)dx : f (x – c)dxr. a a+c Explain this result geometrically.

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Q: L {lostt sin ţ t}

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Q: 6. Show that if f : X Y and g : Y → Z are both onto then fg : Z -→ Z is onto. (Note this is function…

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Q: For each of the following: a) Determine the intersection points. b) Draw a sketch of the graph. c)…

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Q: 18. A function f(x, y, z) is called harmonic in a region D in space if it satisfies the Laplace…

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Q: Find the matrix of the quadratic form. Assume x is in R?. a. 3x - 8x,x2 + 2x3 b. 5x, + 18x,x2

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Q: e Stokes' Theorem to evaluate o F dr. F(x, y, z) = z²i + 26xj – y°k ere C is the circle x? + y = 1…

A: Line integral of the vector point function

Q: 9. Show that the function f:x V-1 is a ring homomorphism f: Z[x] C. 10. What is the kernel of f?…

A: Given: The function, f:x↦-1, which is a ring homomorphism f:ℤx→ℂ.   To determine: The kernel of f…

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Q: Calculate the flux of the vector field through the given surface.  F = 2i −3j + 6x2yk through the…

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Q: B. Find the area of the region bounded by the following: 17. r=3sin 40

A: Here we can use the formula for the area of polar curve which is given as follows A=∫∫A r dr dθ

Q: Find sine half range for f(x) = \cos xl for -1<x<1 COSX for 7 < x < 0. f(x) for 0<x< 7. COSX

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Q: From the list below find the only differential equation that has both functions ₁(t) = e²t and y2…

A: Given solutions of differential equation are y1(t) = e2t ,   y2(t) = -2e2t

Q: Question 1: 259 11 12 (hours) L (t) 15 40 24 68 18 (cars per hour) The rate at which cars enter a…

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Q: Let f: R2 → R be a function given by x²–y² if (x, y) # (0,0), f(x, y) = if (x, y) = (0,0). Using…

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Q: Suppose that µ is the measure defined in item 3. What is µ(O) where O is the set of natural odd…

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Q: Complex Numbers. Find, in the forn x + iv. showing the details: 16. (1 + i)12

A: Given complex number is 1 + i12

Q: b) Let U = {(x,y,z) : 2x+3y +z = 0} and V= {(x,y,z): x + 2y-z = 0} be the subspaces of R3. Find a…

A: This is a problem of linear transformation.

Q: Peronve:- de of Giuen:- a - epper helf filare f(2)16 anatytic fan in d+ iB în -R R X ufper helf óf…

A: Consider ∫Cfzz-α2+β2dz=∫Cgzdz Where C is a contour as shown in the figure gz=fzz-α2+β2 Poles of gz…

Q: B2. Euler's Theorem Let G = U(n) %3D Prove For any a in G, a^m = 1 (mod n), where m = (phi) (n),…

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