Find the solution of the following heat conduction problem using the variable separation method. (0 0) ôt T(0,t)=0, T(1,t)=1, (t>0) %3D T(x,0) = 2x – x², (0

Q: (f) Consider the functions y= V7 and y = r² on 0 <I<1. Determine the length of the longest…

A: We will find length of horizontal line between two given curve in terms of a single variable and…

Q: Find the area of the shaded region. r = V cos 20 r = 9 cos 0 NOTE: Enter the exact answer. A =

A: We have to find the area under the curves r=cos 2θ and r=9 cosθ

Q: Let f(x)=x5−6x2+7. Compute the value of the Taylor polynomial of order 7 centred at x0=1 of ?f(x)…

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Q: A = [-2,4,-2,-4,        2,-6,-3,1,        -3,8,2,-3,        0,2,5,3]  Find a non-zero vector R^4…

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Q: Which of the following should replace the question mark to complete the series?* 日日日 O Option 4…

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Q: 8. Let d denote the discrete metric on a set X. Let (n) be a convergent sequence on (X, d). Which of…

A: Given d is discrete metric on a set X. and (xn) is a convergent sequence on (X, d).

Q: Find the root of the polynomial f(x)=x' - 5+ 3x using Bisection method. Iterate until f (c, )<e =…

A: Hope you like it

Q: Solve the following initial value problem over the interval from t = 0 to 1.5 where y(0) 1.3. What…

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Q: Let A = {1,2, 3, 6}. Define a relation R on A as follows: x Ry if y – x > 0 Write out the relation R…

A: We have to find the relation and write as set notation.

Q: roblem 1: Prove A = {m E Z :m mod 6 = 2} is a proper subset of B = {n E Z : n is even}. roblem 2:…

A: We have to prove that the given statement in question 4.

Q: Jo x² +6x+10 n of the trapezoidal ru idal Lru Owit

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Q: Question 2: Find the inverse Laplace transform of 10 a) F(s)= s(s+2)(s+3)? b) F(s)=- s? +4s+5 1 -2s…

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Q: By hand, use Cramer's rule to solve system i above

A: # As per the guidelines we are entitled to solve one question at a time , Please resubmit the other…

Q: 5. In the differential equation (1+3xsin y dx– x² cos ydy = 0, we let the substitution %3D

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Q: Vignesh owns a cottage in the shape of a cube with each edge of length 26 feet. The roof is in the…

A: Given: Roof is a square pyramid. Lateral side of the square pyramid is 17 feet. Height is 2 feet.…

Q: d) 3/2 d.x (x4 +1)2 16 Cos(2.r) T e) dx %3D 1+ x2 e2 8. 8. sin x d.x (x2 + 4)(x - 1) Cos 1 - |

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Q: Use the triple integral to find the volume of a solid G enclosed by surfaces x = y*2 and planes…

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Q: Find the volume of the solid generated when the region enclosed by y = Vx, y = 6 – x, and y = 0 is…

A: The volume of revolution of the area bounded by the curve f(x) and the x-axis between the limits x=a…

Q: Each student in an international study group speaks English,Japanese, or Spanish. Of these students,…

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Q: (a) (1264)11 (c) (352)(136)(1254)102 (b) (125843)53 (d) (348)(456)*(1325)10

A: We have to find a 126411 and d 3484565132510

Q: Determine the osculating circle of the helix defined by y = x^3 − 3x + 1 at x = 1.

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Q: Solve using Jacobi's iteration The following system of equations is designed to determine…

A: We Know that  Jacobi method is one the iterative methods for approximating the solution of a system…

Q: 2. Let W be the portion below the plane z = centered at the origin in R3. Give a domain for…

A: We will use relation between cartesian and spherical co ordinate to find domain of W

Q: olve the following differential equations using the substitution suggested by the equation.

A: We have to solve the given differential equation.

Q: 4х — 6 2. Let f(x) = 1- (2х — 3)3 a. Find the Taylor series representation for f about x = 1.5 that…

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Q: a) Find an equation of the sphere with center (1.-3,-5) and tangent to xz-plane.

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Q: In the differential equation (6x – 3y +2)dx-(2x – y-1)dy=0, we let the substitution dx =

A: Given differential equations is non homogeneous differential equation.. We have to find the…

Q: 4. Locate the centroid (x, y)of the following composite areas: b) 3 ft 3 ft 1.5 ft 1 ft

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Q: Evaluate: C(25, 4) + C(30, 3) + C(35, 2).

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Q: Find an equation of the plane containing the line a = 3t, y = 2 – 4t, z = 1+t and parallel to…

A: We have to find the equation of the plane containing the line x=3t, y=2−4t, z=1+t and parallel to…

Q: 14x10* 1. The velocity of a rocket is given by v(t) = 2000 In -9.8t,0<t<30 where 14x10ʻ – 2100t v is…

A: According to guidelines we can solve only one question.

Q: Below is a sketch of the graph of f. Find: lim f(x) lim f(x) lim, 2+ f(x)

A: From the given graph, it is observed that the curve goes to -∞ when x goes to 2 from the left side.…

Q: Using high-accuracy central difference formula, determine the derivative of the function F(x) = x' +…

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Q: 43. Let {rn}-1 be a bounded sequence and {y„}=1 be a sequence tending to 0. Pro that x„yn → 0.

A: We have given that , xn be a bounded sequence. Also , yn be sequence tending to 0. We need to prove…

Q: 1. Let r be pasitine ou a N_alg m measure * A, A, A3EM aud mirwire dijoint The (A3)

A: I have used the definition of measure to show this.

Q: Give some examples of geometric problems that can be solved using the parametric equations of a line…

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Q: 2. Let f be continuous and differentiable everywhere. Suppose that f has zeros at 1 and 3. Show that…

A: Given that                    f be continuous and differentiable everywhere. Suppose that f has…

Q: y ct) = sin 2t cos 34

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Q: 49. Let {x,}=1 be a sequence of real numbers such that xn Calculate lim,∞ exp(cos(x, – 1) – 1).…

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Q: Determine the first three nonzero terms in the Taylor Polynomial approximation for y' = cos x + e2x,…

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Q: Show that the column vectors (1,1,2,4), (2,-1.-5.2), (1.-1,-4,0) and (2,1.1,6) vectors in R are…

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Q: Using high-accuracy central difference formula, determine the derivative of the function F(x) =…

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Q: where p Let W be the set of all vectors of the form is a negative integer and q is a positive…

A: Given W be thr set of all vectors of the form pq, where p is a negative integer and q is a positive…

Q: Which of the following contains both radial and bilateral symmetry?* Butterfly Human body Sunflower…

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Q: Use the Adams-Bashforth-Moulton method to approximate y(2.4), where y(x) is the solution of the…

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Q: b. Use the result in item 2(a) to find the 4th degree Taylor polynomial of ƒ about 1.5. c. Use the…

A: This is a problem of Taylor's theorem.

Q: Laplace and Inverse Laplace Transform -3t Solve the Laplace of e COS Tit

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Q: Define two vector functions 7(t) = 2 sin(t)i + 8 cos(t)j + t°k ü(t) = 8 sin(t)? + 2 cos(t)j + (t? –…

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Q: Look for or create your own set W that is a subspace of R' or R.

A: We create a subspace of ℝ3.

Q: Solve the following equation byCramer's rule and find the value ofx, y, z. 3x + y + z = 3, 2x + 2y +…

A: The given equations can be expressed as ,  3x + y + z - 3= 02x+2y + 5z + 1 = 0x - 3y - 4z - 2 = 0 We…