Find the boundary of the sequence xn in the normalized vector space C [a, b], if it exists. 4 cos 3 t 2.11. a = -5n, b= -4n, x„(t) 5+ cos" t

Q: 1 (a) Draw a direction field and sketch a few trajectories. (b) Describe how the solutions behave as…

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Q: Find order and degree of y'+(y")? =(x+y")² а. 1,2 O b. 2,1 О с. 1,1 O d. 2,2

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Q: Without finding T and N, write the acceleration of the motion a(t) to the position vector r(t) =…

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Q: Which of the following is not true for the differential operators A, B, and C? A (A+B) +C = A+ (B+C)…

A: Differential operator

Q: (z/(u + m) = d)dĒшAuA (! h) 3n3m(n+m=4^n-m=2) (1=m-uv+=+u)шEUE (8 (S=₂+₂)Ẹи (ə (0 = m+u)шEUA (³ (m>…

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Q: Suppose that f: R² R² is a function such that f (1,2)= the linear approximation. (Use syntax like…

A: We have to estimate f (1.1, 2.01) using the linear approximation.

Q: . (Section 14.4) Let curve C be described by vector function(t) = (cost-1, sint, 3/2) on 0 ≤ t ≤ b.…

A: The curve C is defined by the function,on the interval,The length of the curve on the given interval…

Q: v : {p, q, r, s, t, u} formula (t → g)A (u → p) A (T → s) ^ (tAg → r)A (s t)^ (uAp + 1L) Find an…

A: Given that v:{p,q,r,s,t,u} to {0,1} It satisfies a formula, (t→q)∧(u→p)∧(T→s)∧(t∧q→r)∧(s→t)∧(u∧p→⊥)

Q: Which functions form the basis of solutions for the ODE y – y" – y" +y' (x) = 0? O {1, e ?, e², æe }…

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Q: If F(s) = 1/(S-2), then f(t) is %3D a) e²'u(t) c) u(t-2) d) e"'u(t) -2t b) u(t +2)

A: Given Fs=1s−2 We have to find the ft Use definition of inverse Laplace transform, which is given…

Q: 2. Consider the vector-valued function R(t) = Show that is continuous at t = 1. (e¹-², 1-1², (2-1)),…

A: We use the sequential definition of continuity to show that $R(t)$ is continuous at t=1. The…

Q: Determine where the vector function r(t) = i + (14t) j is continuous. Use symbolic notation and…

A: Please see the below picture for detailed solution.

Q: If x and y are two n-vectors, then prove that 1 1 (a) x'y< I,l»,- +=1 (Holder incquality) P 9 (b)…

A: Answer :- A) Ans :-

Q: Find an expression for a unit vector normal, no, to the surface x = (4 – cos (v)) cos (u), y = (4 –…

A: The complete solutions are given below

Q: Q2// B :- If u+v3e"cos y and u- v=e' sin y find the Jacobain of the function alu,v at dx.yl (x.y)…

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Q: Find r'(t), r(t,), and r'(t,) for the given value of to- r(t) = (5 + t)i + t°j, to = 1 r'(t) = r(t,)…

A: To find r'(t) and to sketch the curve represented by a vector-valued function and sketch the…

Q: 10. A drop of water falls on the surface z³x+z¹y² + x²y³ = 79 at the point (3, 2, 1). Find a three-…

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Q: The local Game Shop has 120 board games, and 46 video game titles each of which works on one of 5…

A: We have 46 video game titles that work on one of the 5 video games systems.

Q: xye-(2²+v°+z*). Find all points (x, y, z) such that Vf(x,y, z) : Question 2. Consider the function…

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Q: X 7. Give a condition on the vector Y 2 such that it lies in Span {[1] 2

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Q: Find the unit normal vector for the vector-valued function r(t)=(t^2-3t)i + (4t+1)j and evaluate it…

A: Given data:- Vector-valued function, rt=t2-3ti + 4t+1j Evaluate at t=2

Q: Consider the function f(x, y) = 3 Find Duf(4, 3), where u = (a) v=i+j Duf(4, 3) = -1/3-1/10.3 2…

A: Since you have posted multipart question and we can answer three subparts. So, answered the first…

Q: 2. Let x'= [5, 1, 3] and y' =[-1, 3, 1]. (a) Find the inner product, y'x. (b) Find x- - 2y. (c) Find…

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Q: Find a vector-valued function whose graph is the plane x+y+z= 12, O r(u, v)=-ui-vj+(12-u-v)k O r(u,…

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Q: z = f(st – 3, s+t°) and fi(-1,9) = 3, f2(-1,9) = 7, fu(-1,9) = f12(-1,9) = f21(-1,9) = fz(-1,9) = 2.…

A: (b) Apply the chain rule, ∂z∂t=∂f∂x×∂x∂t+∂f∂y×∂y∂tNow differentiate partially with respect to…

Q: Determine the real number \( \alpha \) u x v and î áre orthogonal, where u = 3î + ĵ – 5k and v = 4î…

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Q: - In(a°y*) + x2 Consider z as a function of the variables x, y which is denoted by z and let P(1,-1)…

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Q: Consider a regression model: t = 1,2, ..,T Yt = Bo + B1x1t +U; u = pu,-1 + vi where v,~iid(0, o?).…

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Q: Use the substitution u=-3x+2y to solvethe differential equation (-3x+2y) y'= - 1. a) Clearly…

A: Given differential equation is: -3x+2yy'=-1. Let, -3x+2y=u. Differentiate both sides w.r.t. x.…

Riemann Sum

Riemann Sums is a special type of approximation of the area under a curve by dividing it into multiple simple shapes like rectangles or trapezoids and is used in integrals when finite sums are involved. Figuring out the area of a curve is complex hence this method makes it simple. Usually, we take the help of different integration methods for this purpose. This is one of the major parts of integral calculus. 

Riemann Integral

Bernhard Riemann's integral was the first systematic description of the integral of a function on an interval in the branch of mathematics known as real analysis.