Given that (1 COS 4.r) x2 a, if x = 0 if x < 0 f(x) げx> 0. J 16+ Vx -4 If f(x) is continuous at x = 0, find the value of a.

Q: Q4 Evaluate the following integrals cosh? (=) dx -In2 1 - fe 2 - cosh(lnx) dx

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Q: 1. The square of the tens digit of a two-digit number is 7 less than the sum of the digits. If the…

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Q: 1 Expand f (z) = in the domain 4 < |z| < 12 (z-4)(z-12)'

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Q: Which of the followings can be considered as integrating factor for the differential equation xdx +…

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Q: y² = 9 - x² and ミ1、22 9. 9.

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Q: 2 2 5. Find the volume of the solid bounded by the surface f (x, y) = 3x´y´ and the curves y = 2x -…

A: We will have to find the volume of the solid bounded by the surface f(x,y)=3x2y2 and the curves…

Q: 24. If A and B are nonzero vectors, prove that the vector A- cB is orthogonal to B if e= A· B/|B.…

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Q: Find the volume to the nearest whole number.

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Q: Consider the following sequence: gi = 3 92 = 5 3 * gk–1 – 2 * Ik-2 Ik %3D for cach integer k > 3…

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Q: Q 2- use Newton-Raphson method to obtain a root of equation x'- 2x + 3x -5 = 0 %3D

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Q: 6Chair made in 2 houss how

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Q: Q11 (aitı-) is sub field of (Riti.) O (OFi) is a sub of f

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Q: y'+ty13=tan(t),      y(−1)=−1y′+ty13=tan(t),      y(-1)=-1 a) Rewrite the differential equation, if…

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Q: 17. To each person on the earth assign the number which corresponds to his age. A. bijective 18. To…

A: NOTE: Since we only answer up to 3 sub-parts, we’ll answer the first 3. Please resubmit the question…

Q: Determine if the statement below is true or false. Justify your answer. If f"(c) = 0, then (c.f(c)…

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Q: If A is a Hermitian matrix then A + jI is invertit Select one: True

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Q: 22 The cost of producing x units of a product is described by C(x) = 100 + 40x. What is the total…

A: the cost of producing x units  given cost function C(x) = 100 + 40 x

Q: (a) Determine radius of convergence of this power series. (b) Determine whether this series…

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Q: 2. Let n be a natural number and let A, B E Mnxn(C). If AB = 0, does it follow that either A = 0 or…

A: Given :  A, B ∈ Mn×n(ℂ)  with  AB = 0. To find : We have to examine whether  A=0 or  B=0.

Q: Exercise 4: Solve the heat equation on the square [0, 7] × [0, T] subject to the following bound-…

A: The given problem is to solve the given two dimensional heat equation partial differential equation…

Q: Question 2 Let z, and z, be two complex numbers such that z, = 3+ 4i and zą = 2 – 2i. Compute the…

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Q: For the right triangle belowr = Select one: a. Vx? – y2 b. Vx +y C. x? + y? d. Vx? + y?

A: Given : We are given a right triangle with hypotenuse(r),  base(x) and perpendicular(y). To find :…

Q: Q1/ (Qti.) is sub field of (Rit,.) O (nFi) is a sub of f. © (UFi) ia suboff.

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Q: Change the independent variable to determine a first integral of the functional: • 02 01 Let v'(1) =…

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Q: Clearlake optical has a $50000 note due in 3 years. The owners wish to create a sinking fund to pay…

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Q: (1) Suppose that f and g are multiplicative functions. Prove that the function F defined by I…

A: Consider functions f and g to be multiplicative functions. To prove that function F defined by…

Q: Solve the following numerical problems and provide all your pertinent solutions: Sketch a graph and…

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Q: et y" – 2y' + y = 1+ x2 -here y' = ) dy dx

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Q: Consider the system below. i = rx + y – x³3 ÿ = -x+ ry – 2y3 This system has a fixed point at (0,0).…

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Q: Q3) Given the following Z-transform which is factored using partial fraction expansion, then В + z2…

A: Solution

Q: Using Laplace transforms, solve the differential equations (D+ 1) y, + (D- 1) y2 = e- (D+2) y, + (D+…

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Q: Prove that ord,(a + b) > min(ord,a, ord,b) with equality holds if ord,a ± ord,b.

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Q: 3. Let A and B be m x n matrices and || · || be any matrix norm for m x n matrices, prove that | A||…

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Q: Expand f (2) = Tnin powers of (z – 11). Also clearly mention the domain in which this expansion is…

A: For the solution of the problem follow the next steps.

Q: find the laplace transform of the following 1. L [2t2e-3tcos(4t)] 2. L [2t2e-3tsin(4t)]

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Q: Q2-use Newton-Raphson method to obtain a root of equation x'-5x+3+0

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Q: Find the solution. dy 2y dx A y = x?(x-c)-2 B y = x³(x+c)3 y = x (x+c) D y = x²(x+c)2

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Q: 7.H Jse the divergence theorem to evaluate where S is the sphere x+y? +? = 4 oriented with outward…

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Q: Expand f(2) = z-5)(=-15) in the domain 5 < |2 < 15 .

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Q: 10) The following results are from a regression where the dependent variable is COST OF COLLEGE and…

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Q: 3. Lagrange Interpolating Polynomial (. Find the second degree Lagrange Interpolating polynomial…

A: Given, f(x)=sin(πx)x0=1 , x1=1.25 , x2=1.6 To find: Second degree Lagrange Interpolating Polynomial…

Q: The owner of oak hill squirrel farm deposits $1000 at the end of each quarter into an account paying…

A: The owner of oak hill squirrel farm deposits $1000 at the end of each quarter into an account paying…

Q: (3) The von Mangoldt function A is defined by log(p), if n = p*; where p is a prime, and k > 1; A(n)…

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Q: Find the Cortesían coordinates of the' point P with polar coordinates CG,Ę)! 6 6) Find the equation…

A: (a) To find the Cartesian coordinates of the point p with polar coordinates as 6,π6

Q: Given the area in the first quadrant bound by x²= 8y , the line x= 3 and the x-axis. What is the…

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Q: With the following system of equations 3 x+2 y = 4.5 2x+ 3 y-z = 5 - y + 2z = - 0.5, set up the…

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Q: -5 2 QUESTION 13 Let A -6 4i -3i -3 2 1 3 -14 11 0 -2i Write down the eigenvalues of A? and their…

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Q: Σ n(n + 1) (n + 2)! Use (a.) to show that f(x) dx (-2)"-1. n=1

A: We have to find the power series of f(x).