The expression 10 C2 is equivalent to 10! 8!2! 10! 8! 10! 2! 90

Q: The antiderivative of f(x), denoted by FX), exhibits an odd symmetry i.e., it satisfies the property...

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Q: 1. Derive the 5th degree MacLaurin series expansion of f (x) = 1- 2x

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Q: Which one is the next figure in the series? ...

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Q: LOCATE THtE NUMBERS 2 and z, vectorially (show your illustraton), APD uSE THっE vもCtDes TD 千ND A) 2,+...

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Q: Find the roots: x5 = 4i

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Q: Find the maximum value of f(x,y,z)=y-z subject to x+y+z=1, x^2+y^2=1.

A: Let us consider the function f(x,y,z)  To determine the maxima subjected to g(x,y,z)=0 Find the lan...

Q: iv) Fix some a e R. With f(x) = sin(x) as before, we define a new function g: N→R such that g(n) = f...

A: Since you have posted a question with multiple subparts with some parts are removed by red lines and...

Q: 2. Use spherical coordinates to find the volume of the solid that lies above the cone z = 3r2 +y? an...

A: Relation between cartesian and vector form  x = ρ sin φ cos θ , y = ρ sin φ sin θ  , z = ρ cos φ  Wh...

Q: Use Stoke's theorem to evaluate the integral curl F. dS where S is the surface given by z = e1-a²-y ...

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Q: (1 3 2 3 2 4 Question 3. Consider the matrix A = . Is there an orthogonal matrix P and a diagonal ma...

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Q: a) Find the length of the curve y(x) = x³/2 /3 – a/2, 3 sa<4.

A: Since you have posted a multiple question according to guildlines I will solve first question (a) fo...

Q: dx - In(F(x))+C. What is F (3) if C=0? For (x+x) (xtan-'(x) +1) A

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Q: 2. y' +y = ee ||

A: Given that  y'+y=eex We have to solve the above equation.

Q: 1 Let an = n > 3. 3/ nvlnn (a) Show that the sequence {a,} is decreasing. n=3 (b) Without computing ...

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Q: 2-A card is drawn at random from a deck consisting of cards numbered 2 through 10. A player wins 1 d...

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Q: 7.

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Q: Given the orthogonal basis B for R4 and the vector v below, find the Fourier coefficients for v with...

A: Given  we have given the orthogonal basis for R4 and the vector v below  B =1-21-2, 10-10, 4-347, -2...

Q: dy/(3x2) = (1 + y²)1.5 dx.

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Q: Find the volume of the solid formed by the region inside the sphere x2 + y² + z² = 16 and outside th...

A: The given problem is to find the volume of the solid formed by region inside the sphere and outside ...

Q: Evaluate e f'(x) sin f(x) dx. Your answer should not contain f, which is a differentiable function w...

A: Some of the properties of integration  If I=∫f'(x) g(f(x)) dx then using substitution t=f(x) then t...

Q: Can 199 cannot be written as the sum of an even integer and two odd integers. Show prove too.

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Q: If m` E = 0, then E is measurable.

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Q: ABCD is a cyclic quadrilateral and AB and DC are produced to meet at Q, and BC and AD are produced t...

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Q: 3. + ¿322 Simplify, i2016 + ¿2017 4. Evaluate, ¿15 (2+ i) (-i**) 3+i13

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Q: 1. Let x, y ∈ Z. Use a direct proof to show that if x + y is even and x is odd, then y is odd.

A: As per the company rule, we are supposed to solve one problem. Therefore kindly repost the remaining...

Q: Question 19 (2-sec?x) sec'x sec( 34 -x) e In (n/c) What should be the value of A for x to be integra...

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Q: (2- sec?x) elm cale sec³x sec( 3A – x) cIn (ale) Nhat should be the value of A for -dx to be integra...

A: We will use options to find the answer .

Q: = 0,0 < x < a,0 < y < b dy dx² и(0, у) 3D 0, и(а, у) 3D 0,0 <у <b u(x, 0) = 1, u(x, b) = x, 0 < x < ...

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Q: Problem 6. Show that if AB = AC and A is nonsingular, then the cancellation law holds; that is, B = ...

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Q: Suppose that f is a function such that f' (c) = 1 for some number c in the interval [a, b]. Is it po...

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Q: 8. Which one of the following statements is NOT true about this graph? F D Figure 1 O A) There is a ...

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Q: Sketch the graphs of the following functions. 1 (i). f(x) = x 3 (ii) f(x) = x + x? (iii) f(x) x? - 1...

A: We have drawn graph of each functions by hand . 

Q: Hint: This follows easily from a certain string of inequalities; E 1-14 is relevant. *39. Suppose ƒ ...

A: We will use concepts of  Riemann integration 

Q: log(2 + (3 * i))^e =

A: Consider log2+3ie. We know that logx+iy=logx2+y2+itan-1yx and logza=alogz. Therefore log2+3ie=elog2+...

Q: 1. Graph the following set on a number line and express the set in interval notation. {xdxs -2} -10 ...

A:     Given :Graph the following set on a number line and express the set in interval notation {xIxS≤-...

Q: Anthony is twenty years older than Brenda. Five years from now, the sum of their ages will be 42. Ho...

A: We want to find age of Anthony.  

Q: Determine whether the given series is convergent or divergent. 5" + sin? n (a) 3n – | sin n| n=1 +oo...

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Q: The comlex number below when represented is (-V3+3i)(1-i) (3+/3i)(i)(/3+v3i) O In the second quadran...

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Q: 2.) Calculate the curve integral over the vector field V (xr, y)

A: The curve integrals in the form ∮CVxdx+Vydy involve the integration over a specific path C. In this ...

Q: Question 33 Evaluate (~p q) -→~(rV ~q). O TTFFFFFT TTTEFFTT O TTFFFTTT O TTFFFFTT O TTTFFTTT O TTTTF...

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Q: 1 Let an = n > 3. nInn (a) Show that the sequence {a,} is decreasing. (b) Without computing any limi...

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Q: Question 1. Suppose that A E Mnn is an orthogonally diagonalizable matrix with n different eigenvalu...

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Q: 67x86=

A: Solution

Q: Problem 7. Prove that if A is symmetric and nonsingular, then A- is symmetric.

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Q: Let x, y ∈ Z. (a) State the contrapositive of the statement: ♠ If xy and x + y are even, then both ...

A: Contrapositive for the statement "if A then B " is "if not B then not A" Given statement:   If xy an...

Q: Match the differential equation with the appropriate slope field. y' = O A) B)

A: Note: We know that, the slope field is a visual representation of the solutions of a first-order dif...

Q: What type of reasoning is being illustrated in the following example? All even numbers end with 0, ...

A: It can be considered that an assertion or fact is given as ''All even numbers end with 0, 2, 4, 6, o...

Q: dx For - = In[F(x)]+C• What is f(/3) if C = 0? (x+x³) (x Tan-'x + 1) -1 - 6. + -1 - -15 -is -is

A: Integrate ∫dx(x+x3)(xtan-1x+1)

Q: Find the surface area of the following figure. Round your answer to the nearest tenth. 14.2 m 11 m 1...

A: Clearly, the given figure is a pyramid.And we know that the surface area of a pyramid is: S=B+12P·l ...

Q: 1. Fibonacci Numbers Recall that the Fibonacci numbers f(n) can be be defined recursively by letting...

A: We will  use strong induction method to prove S(n). Where S(n) is: f(n)=1+52n-1-52n5, with f(n)=f(n-...