Q1) Using the definition of continuity prove that the functions are continuous 1 fox)=x²³² +1 it x=2 2 f(x) = 1 it x = 2 3 f(x) = it x = 1 X-1 A x² +1

Q: IV.Sketch the ff. curves: Find all its properties.

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Q: Find the Fourier Series of the given f(x), in which the periodicity is 27 f(x) 0 if -≤x<0 sin x if…

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Q: 4) Find the total derivative of the function: a.f(x, y) = ex²+y² 1 c. T(l,g) = 2₁ 2TT. b. z = x siny…

A: Total derivative of a function f(x,y) is given by df=fx dx+fy dywhere fx=∂f∂xfy=∂f∂y

Q: x-y -dA over a square region Using the transformations u=x-y and v=x+y to evaluate R Rx+y with…

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Q: Evaluate the multiple integral ay d.A where D is the region in the first quadrant bounded by the…

A: We want to find the form of given integral

Q: 2. Gauss-Seidel's Method. Stop at 4th iteration. (correct to 3 decimal places) 15x + 3y - 2z = 85…

A: Use the procedure of Gauss Seidal method with initial guess (0,0,0) to proceed further as in next…

Q: Find the Laplace transform of the following: 1. y" + 2y' + 5y = t cos(5t) - 6, y(0) = 1, y'(0) = -2

A: To find the Laplace transform of the problem.

Q: y" - y' - 6y=t²e³t — 4t², y(0) = 0, y' (0) = -1

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Q: F[x₁,...,n] is an integral domain.

A: Solution:-

Q: Let f(x) be an irreducible ow that all roots of f(x) =

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Q: Problem. A garment factory manufactures men's shirts and women's blouses. The production process…

A: The following steps are used to find the solution of the linear programming problem by graphical…

Q: Two different printing companies will print T-shirts if the design is submitted by the customer.…

A: Given that two different companies will print T-shirt. Magic printing company charges a $50 set up…

Q: Consider a point in Cartesian coordinates given by (3√3, -3, -8). (a) Find a corresponding…

A: conversion formula from cartesian (x, y, z) to cylindrical coordinates (r, θ, z) r2=x2+y2tanθ=yxz=z…

Q: 24. In order for a linear programming problem to have a unique solution, the solution must exist OA)…

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Q: y"" - 4y" + 5y' - 2y = 7t-5, y(0) = 0, y'(0) = 0, y'(0) = -2

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Q: Question 2 Difference equations, Laplace transforms and the Calculus of Variations. a) Suppose we…

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Q: Let C be the curve of intersection of the paraboloid a² + y² = z and the cylinder +(y-1)² = 1 (a)…

A: Given that C is the curve of intersection of the paraboloid x2 + y2 = z and the cylinder x24 + y -…

Q: Find the Laplace transform of the following: t, 1. g(t): (t - 4)², (9t - e20-4t t<3 3 ≤t<5 t≥ 5

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Q: Find Maclaurin series for the following functions 1) e-sx Ans. n=0 (-5.x)" n!

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Q: Find the value of (D) solve in detail 1.85 1219 = = 20.88 (0.015/60). 4.87 D' *

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Q: (a). f(x,y)= ln(2xy-11), 1 (b). f(x,y)=- √√16-x² - y² (c). f(x,y)=√√9-x²-y².

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Q: Consider the function defined by f(x, y) = y + √x + 2. (a) Find the domain and range of f. (b) Draw…

A: This is the question of multi-variable calculus.

Q: create 2 sample word problems of basic rules of differentiation  with solutions

A: First problem: At what rate is the area of square increasing when the side increases at a rate of 2…

Q: Root-finding techniques Bisection • Solve for the root of f(x) = sin 4x if x₁ = -2 and x = −1

A: Note:- As per our guidelines, we can answer the first problem as exactly one is not mentioned for…

Q: Solve 1 + 7xdx manually

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Q: 10. The region is bounded by y = x³, y = 2x + 4 and y = -1. Then Arearegion = [*f(x) dx + [° g(x)…

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Q: 1. Prove the following using a truth table. {℗ is a symbol for XOR.) p@q = (pvq) ^ (p ^ q)

A: We will make the Truth table to show the given two statements are equivalent.

Q: Consider the integral function J(m, n) = √² co cos™ (0) sin" (0) de with integer m, n. i. Evaluate…

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Q: Calculate the following. Σ=30: i=30 3 + 4i I. 1 II. + …+ 1 512 16 LIT + 1 4 118 +

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Q: 2. g(t) t, (t-7)², (11t-e21-30, t< 4 4≤t<7 t27

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Q: 3. Let V be a vector space over C and let L: V→ V be a linear transformation. (a) Give the eigenval…

A: Introduction: An eigenvector or function vector of a linear transformation is a nonzero vector that…

Q: 19-f(t)=t-sin 2t; 20-f(t)=e" cos 2t.

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Q: 9. Use the shell method to find the volumes of the solids generated by revolving the shaded region…

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Q: (A^¬BA¬C) logically follows from A (1) -C (2) -Av-B (3)

A: This is a problem of Logic.

Q: Determine the time required for the bacteria concentration to be reduced to 5 using Newton's method.…

A: As per the question we are given the equation for the bacteria concentration c as a function of time…

Q: Complete the table of values below. Then, sketch the graph of r = 2 - 3 cos in polar coordinate…

A: We know that a polar coordinate is represented as r, θ, where r is the function of θ and θ is the…

Q: 2. Solve the yk+2+9yk = 4k + cos 3k using method of undetermined coef- ficients.

A: Introduction: All the phrases withinside the connection or equation have the equal traits while we…

Q: The figure shows the flow of traffic (in vehicles per hour) through a network of streets. X1 400…

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Q: f(x) = 4xe-2x+3x √5x ; ƒ' (2)

A: Use the following finite difference formulae, to compute the first derivative of the function fx.…

Q: Problems. Show complete solution and find the answer. 5. A wheel turns through an angle ( radians…

A: 5 Given that angle θ=128t−12t2 and t=4 sec. We have to find the angular acceleration in radian per…

Q: I need the answer as soon as possible

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Q: 4. Let V be a vector space over C and let L: V → V be a linear transformation. State the definition…

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Q: Solve the equation [2]17 X + [10]17 = [13]17 X + [12]17 for X ∈ ℤ17. Write your answer as X = [x]17…

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Q: a) rsine de + (r3-2r² cose + cos0)dr = 0.

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Q: 3. Transform the following to Laplace equivalent a. y(t) = of усь +0 5 -66 3 b⋅ y ≤t) = 100+ € ² +…

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Q: The Laplace Transform of the figure below is in the form as shown. Find - b. Answer must be an…

A: This is a problem of Laplace transform.

Q: Points D(z), E(2₂) and F(z,) lie on a cir E and F intersect at A, B and C. A, B, C a (a) Find the…

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Q: Find the Laplace transform of the following: t, 2. g(t)= (t-4)², (9t-e20-4t, t<3 3<t<5 t≥5

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Q: QUESTION 2 Let S be the following relation on C: S = {(x, y) = C²:y-x is real}. Prove that S is an…

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Q: Discount ₱15,800 for 11 months at 14.25%simple interest.

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