Prove by induction that Σ₁₁ (5¹ + 4) = (5¹+¹ + 16n − 5) - i=1

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A: Q 21 asked and answered.

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Q: What is the z transform of h(n) h(n) = (1/2), 0≤n≤3 elsewhere a. b. C. d. 0₁ 1+ (1/4)z²+ (1/8)z³ 1+…

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Q: The function v = f(t) satisfies the differential equation dv = k ( - ) dt Where k and h are non-zero…

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Q: Give the best estimate of the output value at the critical point identified above.

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Q: Exercise 12.3.5. Let A: V→ V be a linear map with eigen-pair: (r, A) E V x R. Prove the following:…

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Q: Consider the differential equation 2x2y" + 3xy' + (2x - 1)y=0. The indicial equation is 2r²+r-1=0.…

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Q: 1. Carefully show all work and circle your answer. (a) Use l'Hospital's rule to find lim x sin(π/x).…

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Q: 3. Consider the following optimization problem [201, 202] [1 x₁ + x₂ = 1 0 [2][2]+3,5 [2] minimize…

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Q: Prove by induction that for positive integers n, 4|(5¹ +34n+3).

A: We have to prove by induction that for positive integers n, 4|5n+34n+3.

Q: Find power series and interval of convergence

A: (1) The function f(x)=13+x To find the power series for the function centered at x=0 Further we have…

Q: (a) Set up the integral used to evaluate the line integral using a parametric description of C. Use…

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Q: a drug is produced on 03/01/2023 after 10518 hours the drug degrades by 10%. what is its shelf life

A: Given, A drug is produced on 03/01/2023 after 10518 hours the drug degrades by 10%.

Q: 2) Let assume the set N = {1, 2, 3, ...}. a) Show that the function d(x, y) = 1 X Y defined on N is…

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Q: If , y € R", which of the following is a necessary condition to the equality |||| = ||||? (a) is…

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Q: t 92 + y² b = Tab JE. ( 7 )= (910)+), £€ [0, LT] bomt

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Q: Problem 7.3: Using two methods to find the PS of (x² = 4x - 3y y' = 3x + 4y x(0) = 1 y(0) = 2

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Q: Draw TWO different graphs each with 3 vertices having degrees 1, 2 and 3. Are these graphs the…

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Q: y' = [2 2 2] 2 2 2 y, y(0)= 2 2 2 [For Exercise 8, the characteristic polynomial is p(A) = -A²…

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Q: 8. Explain how to calculate 29 x 20 mentally by using 30 x 20. Write an equation that uses…

A: (a + b)×c = ac + bc

Q: Use the properties of the definite integral to find ľ round. If it is not possible, write NP for…

A: We are given that           a∫b f(x)dx = 4           c∫b f(x)dx = -1     => a∫c f(x)dx = a∫b…

Q: Find the local maximum and minimum values and saddle point(s) of the function. You are encouraged to…

A: The given problem is to find the local minima , local maxima values and saddle points of the given…

Q: Use mathematical induction to prove that, For each integer n ≥ 0, 6|(n³ − n).

A: For each integer n≥0 , 6 n3-n. To Prove: Using mathematical induction prove that 6 is a divisor of…

Q: Use appropriate formulas from geometry to evaluate the integral 14x - 11dx. Write the exact answer.…

A: The integral I=∫03|4x-1|dx To evaluate the integral by using application of geometry. We split the…

Q: Graph the system below and write its solution. x+2y=4 y=-x+1 Note that you can also answer "No…

A: Given system is x+2y=4            .......(1) x+y=1              .......(2) Equation (1) and (2) are…

Q: 12. Maria is working on the multiplication problem 38 x 25. Maria says, 4 times 25 is 100, so 40…

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Q: > Let f(x, y) = 2x a) Express f(x,y)dA as i b) Calculate the integral. 8. ( as an iterated double…

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Q: Solve for Y(s), the Laplace transform of the solution y(t) to the initial value problem below. y''…

A: Given that the initial value problem y''-7y'+12y=6te3t  , y0=2 , y'0=-6  .

Q: n The value ofrC, + P,)is r=1 A B C D n. 2n-1 - 2n-1 n. 1 + (n + 1)! n. 2-1 + (n+1)! - 1 n² +n +5

A: The given function is, ∑r=1nrCrn+Prr To find the value of the given function.

Q: Using Laplace transforms find the particular solution of d²y dr² 6y=14e¹ satisfying y = 3 and = 8…

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Q: Determine an equation of a line that lies directly on the plane: 3x+4y+5z-29=0 . (Justify your…

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Q: For triangle FGH, the measure in degrees of angles F, G, and H are 86, 32, and 3x + 5 respectively.…

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Q: 5. Consider the surface described by the parameterization r(u, v): = ((2 + sin v) cos u, (2 + sin v)…

A: Given in question:- To Consider the surface described by the parameterization    To Find:-  All…

Q: For what value of x does the function g(x) A. x2 -1 C. Ο Α OB OC OD x ≥-2 = 3x³ - 2x² concave…

A: Here, the function gx=13x3-2x2. To determine the value of x does the function g(x) .

Q: Let V₁ = 0 V₂ 2 3 V3 Choose the correct answer below 12 3 and w= 9 Is w in the subspace spanned by…

A: (.)  Given vectors are , v1=   1   0-1  ,  v2=213  ,  v3=1233  &   w=319 vector  'w' is in…

Q: 3. Let B = {[4] [7]} and c={[7][7]} 4 9 C a. Find the change of coordinate matrix from C to B.

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Q: Sketch the graph of a function that satisfies are the given conditions. f'(x) > 0 if x #2 • f"(x) >…

A: The function has the following properties, f'x>0 if x≠2 f''x>0 if x<2 f''x<0 if x>2…

Q: 1. Factor each of the following polynomials completely into irreducible polynomials: a) x² + 1 in…

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Q: Use appropriate formulas from geometry to evaluate the integral √/9 - ²dx. Write the exact answer.…

A: The given definite integral ∫-309-x2dx. We have to find the value of the integral using geometry.

Q: find the derivative of the function. New Section 544 Page 1 y= = x/² √t sirt t dt

A: To solve the problem we use the technique of Leibnitz derivative.

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Q: Find the volume of the solid bounded by the indicated surfaces. the coordinate planes and the planes…

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Q: Consider the surface of revolution H = {(x, y, z) € ¹R³ | x² + z² = (2 + sin¸y)²}.

A: The surface is given as H={(x,y,z)∈R3|x2+z2=(2+siny)2} To find the tangent plane and unit normals…