Use the definition of the functional limit to prove the following: (a) lim 4x + 3 = -5. x→-2 (b) lim x² 0. =

Q: The region S = (x, y (x- 2) + y² < 4 is rotated about the line x = 5.

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Q: Generate the graph of f(x) = x + 2x + 3 with a graphing utility, and use the graph to find a number ...

A: Here to find δ, we can use the epsilon delta definition of continuity which states that: f(x) is con...

Q: Use either elementary row or column operations, or cofactor expansion, to find the determinant by ha...

A: Determinate of the Matrix

Q: 8) A(3,5); 180° clockwise 9) B(-2,3); 180° CCW 10) C(-1,–4); 180° clockwise

A: Please find attachment for the details solution

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Q: 6. (a) Suppose U, W are subspaces of V. Show that (U + W)° = U°nW°. (b) Suppose V is finite-dimensio...

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Q: Let f: ZxZ → Z×Z be defined by the formula f(x, y) = (2x+3y, x+2y). (1) Find the inverse map g = f ^...

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Q: 2. Find the Laplace Transform of t? cos 2t

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Q: Task 1. Using the Eigenvalue method, solve the system x' = Ax for 1 0 -1 0 0 0 2 1 Show that some (n...

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Q: 10. Prove that 7/2 TC sin 0 cos (cos a cosec 0) de 2-a (1-cos a). COS

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Q: A thick spherical shell occupies the region between two spheres of radii a and 2a, both centred on t...

A: The complete solution is in below

Q: Consider the series > (In(2n + 1) In(2n - 1)). n=1 (a) Let a, = In(2n +1) – In(2n – 1). Does {a,} co...

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Q: 4. Construct two circles C, and C, that overlap at right angles and place a point A as described in ...

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Q: 6. (a) Suppose U, W are subspaces of V. Show that (U +W)° = U°n W°. (b) Suppose V is finite-dimensio...

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Q: 23. Find the Laplace Transform of te' sint

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Q: 1. What is the value in the interval [-3,3] so that the difference of the number from its square is ...

A: We'll answer the first question since the exact one wasn't specified. Please submit a new question s...

Q: aces x2 + y2 pint (2, -1, 2)

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Q: Problem 34: Let G be a group. о(а) Show that o(a") = for all a e G %3D (о(а), п) where n is an integ...

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Q: Fundamental Theorem of Calculus 2. Use the definition to show that f(x) = x² is Darboux Integrable o...

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Q: When solving the system below with Laplace transforms, what is the partial fraction expression that ...

A: Laplace transferom

Q: 2. Proof that fis differentiable at x, thenf is continuos at xo By using f(x) – f(x.) = a(r) + B(r)

A: Here we use basic definition of continuous function.

Q: 1) The rational parent function y 1 = - has been transformed. Write the equation of the new image. a...

A: The rational parant function y=1/x has been transformed . Write the equation of the new image .

Q: Find a unit vector u in the direction opposite of (-1,-9, –7). | u =

A: First we find the vector of the same magnitude in the opposite direction of the given vector and the...

Q: H.W: Given the following matrices, please solve the questions below and if you can't solve the probl...

A: Disclaimer: Since you have posted a question with multiple sub-parts, we will solve first three sub-...

Q: 5. Write the formal proof that 2"+2 + 32n+1 is divisible by 7 for all positive integers.

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Q: A 12-meter string is cut into two pieces so that x meters will be used to form a circle and the rema...

A: Here we can note the following  (a) Area of an equilateral triangle with side a = 34a2 Area of a cir...

Q: Convolution method: Find the function whose Fourier transform is 1 (4 + k2)(9 + k²)

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Q: 2. Pinocchio's nose length y (in inches) is dependent on his lie count s. Geppetto has modeled this ...

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Q: • Problem 2. Let a,b e R, with a < b. Consider the set B[a,b] of all bounded functions from the inte...

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Q: dy = 9 + y and y(0) = 4, use Euler's method with h = 0.1 to approximate y(0.6). For dx Approximating...

A: Given: dydx=9+y, y(0)=4 and h=0.1. To find: Value of y(0.6).

Q: onsider the series (In(2n + 1) - In(2n 1)). n=1 ) Let an = In(2n + 1)- In(2n - 1). Does {a,} converg...

A: We will first see whether given sequence in (a) convereges or diverges.

Q: Find the point P such that v = PQ has the components (-1.75, –8.75, 2.5). Q = (1.25, 1.25, 5.5) P =

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Q: Suppose that the function g is defined as follows. 2 if -3.5 <x<-2.5 -1 if -2.5 <x<-1.5 g(x) = if -1...

A: Red line denote the graph of function  draw that whatever given in question its like a greatest inte...

Q: 1. (Row Echelon and Reduced Row Echelon Form). Which of the folowing matrices are in row echelon (RE...

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Q: 2. Determine the 8th derivative of y with respect to x of the function 1 f(x) = 1+x2 and find the va...

A: Taylor series

Q: (3, 2) 1- -2 1 2 3 4 Graph of g' 15. The graph of g', the first derivative of the function g, consis...

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Q: 3

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Q: The degree sequence of a graph is the sequence of the degrees of the vertices of the graph in non-in...

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Q: The degree sequence of a graph is the sequence of the degrees of the vertices of the graph in non-in...

A: We have given that , degree sequence ,  4 , 3 , 3 , 2 , 2. We need to find number of edges. We know ...

Q: A rectangular prism with dimensions 6 m x 4 m x 8 m ( x w x h) is shrinking. 8 m 4 m 6 m Answer the ...

A: Here volume of the prism will be V=lbh So the change in volume in time t will be given by dvdt=lbdhd...

Q: True or False: "Calvin Butterball is a math major." is a statement? True O False

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Q: 4. Let n E N. Find all elements a Zn+1) of order 2.

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Q: Jesse has 4 friends and 5 coworkers. Each day in the year 2021, Jesse talked to some number of frien...

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Q: Use Newton's method to estimate the two zeros of the function f(x) = x -x- 12. Start with xo = - 1 f...

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Q: . Find the Inverse Laplace Transform of the following: f. (s2 + 1)3

A: Use the Laplace transform of predefined functions and first shifting theorem to solve this problem a...

Q: What is the angle in radians between the vectors а %3 (6, 8, -2) аnd b = (-7, 7, 0)? Angle: (radians...

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Q: sin (2?- 4a) lim, 4 sin (x2 – 10x + 24) -10x +24)

A: LHospitals rule indeterminate form.

Q: Jesse has 4 friends and 5 coworkers. Each day in the year 2021, Jesse talked to some number of frien...

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