Find sine half range for f(x) = \cos x for -t< a

Q: Obtain the Laurent series with center zo = 1 for Determine a) The singularity/ies of the function b)…

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Q: * Evaluate. 2t |4 + et| dt

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Q: Find the flux of F = 5zi+ 3y²j+ 2xk through of the total surface of the closed cone y = Vx² + z²,…

A: Flux of vector F through a surface S  can be given by  flux= ∫∫SF.ds We will use Divergence theorem…

Q: Solve the given ODE using the power series method. y'' + xy' + 2y = 0 4. Obtain the recurrence…

A: We have to find Solution of given ordinary differential equation using Power Series Method at…

Q: evaluate the integral where c circle of positive rotation e^z/1 -cos(z) dz where C is |Z |= 1

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Q: What is the correct quadratic function for this parabola?

A: Note: General equation of parabola is y-k = 4a(x-h)^2 and x-h = 4a(y-k)^2  Vertex for both the form…

Q: 15. Consider a simple dice game in which you roll a single die. If you roll an even number, you lose…

A: Solution :-

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: Let 5 Find a basis of the subspace of R4 consisting of all vectors perpendicular to v.

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Q: (a) A = Q = -1 -1 " -1 S D= 10 S T +

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Q: Use the Green's Theorem area formula, Area of R = 1/ 4x dy dy-y dx, to find the area of the region,…

A: We have to find the solution by Green's theorem.

Q: Confirm that the force field F(x, y) = ye"y i + xe"j is conservative in some open connected region…

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Q: B1. (а) The unfinished Histogram and Frequency Table give information about the times, in hours,…

A: Histogram: It is a diagram containing the rectangles, whose base is the range of the intervals and…

Q: Evaluate (2x - y) dx + (x + 7y) dy. C: x-axis from (0, 0) to (0, -7) and (0, -7) to (3, -7) 21

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Q: Consider the solid obtained by rotating the region bounded by the given curves about the y-axis. =…

A: The volume of the solid revolution between the curve  is the volume of the object between  the curve…

Q: Use a proof by induction to prove the following: Let ao = 0, a₁ = 1, and a₁ = (ak-1 + ak-2 + 2) for…

A: We have to prove that 0&lt;ak≤1 for all k using the proof by induction.

Q: B. Find the area of the region bounded by the following: 19. inside /* = 5 sin and outside = 2+sin 0

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Q: Find fF(x), the Fourier expansion of the function f(x) = -1 -1 Σ (1+(-1)"+1) cos(nr2) n=1 fF(x) =…

A: Fourier series of the function

Q: U.S. math SAT scores as a function of household income. 600 538 542 550 554 500 457 475 497 512 528…

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Q: Find the inverse Laplace transform of s+5 s2 +9 Solve for the inverse Laplace transform of 5(s + 2)…

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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: Differentiability of f(x, y) at point (a, b) Let f : R? → R be a function given by if (x, y) #…

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Q: Use a graphing calculator to determine the linear, quadratic, or exponential equation that best…

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Q: Find the orthogonal projection of onto the subspace W of Rª spanned by projw() = v= 4 -2 -13] 3 15…

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Q: Let neN. Set 4, = {n,n+1,n+2,..}and 7 = {ø, A,} pen · a) Verify that T is a topology on N. b) Is…

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Q: what are domine, Vange and null space o F Tisra-s Ty Rom R?into Re 1

A: The given functions are                                 T1:ℝ2→ℝ2 such that T1ξ1,ξ2=ξ1,0.T2:ℝ2→ℝ2…

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: Solve the given ODE using the power series method. y' + xy = 0 2. Obtain the recurrence relation.…

A: Series solution of the differential equation

Q: Use the method of Laplace transforms to solve the given initial value problem, Here, x' and y'…

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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…

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

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Q: 5. Let the universe of discourse be N. Let P(n) be the statement "n2 + 5n +1 is even". (a) Which of…

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Q: 1. What is the sum of the probabilities in any probability distribution? С. 1 d. 2 a. b. infinite O…

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

Q: Proposition. SupposeGis a regular (and simple) graph. If there exists a vertexv∈Vwithdegreeδ(v) = 2,…

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Q: QUESTION 7 Find the area of the region that lies inside both curves. = 8 + 2 sin , r = 7

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Q: Problem 2: Let P₂ be the space of polynomials with R coefficients of degree ≤ 2. Consider the…

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Q: prove the ITT₂TT, ITKITI"

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Q: Find the indicial points corresponding to the series solution of 3xy" + y' - y = 0. 00, 2/3 01, 1/3…

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Q: Let C1 be the circle r = 3 cos 0 and C2 the cardioid r=1+ cos 0. (a) Find all point(s) of…

A: We will find point of intersection by equating both r .  If f is continuous and non negative on the…

Q: Write the equation of a sine or cosine function to describe the graph. D=0

A: Note: General form of sine function is y = A sin(B(x + C)) + D  A = Amplitude, Period = 2π/B  D =…

Q: Chain rule and implicit differentiation Suppose that F(x,y,z) = 0 defines z as a function of x and y…

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Q: a² + 8a + 15 6a² +21a +9 )( a-4a 2a²+9a-5

A: Given expression is a2+8a+156a2+21a+9a-4a32a2+9a-5

Q: 19. inside /* = 5 sin and outside = 2+sin 0

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Q: y? +x = 2, 2r + 3y +3: 6, = 0, y=0, 2=0 TOke the surfaes and obtam valmes fo X, Y and z qnd compore…

A: Given,y2+x=2,        _________(I) 2x+3y+3z = 6, __________(II)x = 0, y=0 and z=0From (I)y = 2-x…

Q: Verify the conclusion of Green's Theorem by evaluating both sides of each of the two forms of…

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Q: Suppose that F(x, y, z) = 0 defines z as a function of x and y and F is differentiable. Prove that…

A: This is a problem of the chain rule and Implicit function theorem.

Q: that

A: Given data  G1 is a solid enclosed by  xy-plane, yz- planes x+2y+z=4 and x-y+z=4x+2y+z=4⇒ z=4-x-2y

Q: LET f:R?->R be a funetion guen by if Cay) + 10,0) i4 ey)=(0,0) Using depinitions op partial…

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Q: 11r If F(r) and o is the surface (x – 4)? + y² + z² = 49 oriented outwards, what is the value of //…

A: We have to find the value of ∫∫σF·ndS where σ is the surface-oriented outwards.

Q: 3. If x and y are two n-vectors, then prove that 1 (a) |x*y|< ]], \»l, - +=1 (Holder inequality) 1…

A: Given that x and y are two n-vectors. We have to prove the following :                          (a)…