Investigate Taylor series expansion. Explain how the Taylor series is used in your calculator to compute values of functions such as sin(x) , cos(x) , and ex , where x represent any value. Write a brief report explaining your findings, and give examples.

Q: Let P denote the path parametrized by r(t) = yz Compute fF.dr, where F(x, y, z) = ( IZ #₁). sin(34)…

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Q: sing the fact that the square bers a and b. ab ≤ (a² + b²). to prove that if a ≥ 0 and

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Q: q= 2 1-4 1 -1 FOR 2X2 matrix, Compute At. - find eigenvalues. find eigen e → compute At > At_V/V…

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Q: If0 sin.x, +sin x, + sin xạ 3 Hence or otherwise prove that if A, B, C are angles of a triangle then…

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Q: 4. for a a = 91(y) = h₁(y, z) a = 2 (y) 9₁ (y) a a = b = = b 9₁(x) = h₁(x, z) = b •9₂(x) h₂(x,z) 5.…

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Q: 1. Sketch the graphs of the two functions f : [0, π] → R, g : [0, π] → R wheref(x) = sin(3x), and…

A: "Since you have asked multiple questions, we will solve the first question for you. If you want any…

Q: (a) Convert to hexadecimal: 1457.1110- Round to two digits past the hexadecimal point.

A: Note: As per company`s policy we can answer only 1 question if there are multiple questions.   We…

Q: Lisa is four years younger than her sister. Which expression stands for the sum of Lisa’s age and…

A: Given: The statement is "Lisa is four years younger than her sister". To write: The expression which…

Q: Each of the following statements is an attempt to show that a given series is convergent or…

A: according to comparison test , if ∑nan , ∑nbn are series with non negative term then (i) if ∑nbn…

Q: If 2x = y² + y ² then express y as an explicit function of r and prove that (x² - 1) d'y dy +x- =…

A: We have to solve given problem:

Q: 3. Find all real numbers t for V = (20 t,4t - 4,5t², t²) are orthogonal. - which = (1,5t,-4t, t³)…

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Q: to estimate the first derivative of the function. Evaluate the derivative at x=1.4 or f'(1.4) using…

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Q: A tank initially contains a solution of 9 pounds of salt in 60 gallons of water. Water with 7/10…

A: Given that a tank initially contains a solution of 9 pounds of salt in 60 gallons of water. Water…

Q: Find z, if z = xyeỹ, x = rcos(t), y = rsin(t), when r = 2 and t 6

A: Consider the provided question, Given z=xyexy,  x=rcost,  y=rsin(t)   when r=2  and  t=π6 We have to…

Q: Question 4 Let R be the region bounded by the curves y = 3x and y = x² + 1 in the first quadrant.…

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Q: 25. y²(xy'+y)(1+x4)¹/² = x

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Q: Theorem. Show that Closed subsets of compact sets are compact.  Need handwriting solution only.

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Q: Subtract in binary. Place a 1 over each column from which it was necessary to borrow. (a)…

A: In binary system, 0-0=0 0-1=1  (borrow 1 as 0-1=-1<0) 1-0=1 1-1=0

Q: If y dy 1 dx = x satisfies the IVP y(1) = 0, then lim y(x) =

A: Given  the IVF as dydx=1x       y(1)=0  first, solve the problem to find y(x) so, dy=dxxnow…

Q: how do you write 98,052 in expanded notation

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Q: Q4) Find Fourier transform of the functions: 1)f(x)= nxl, x π 3)f(x)=xe-x1, x ER 2)f(x) = 4)f(x) =…

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Q: 9. Population of bacteria, P, has a fixed relative birth rate birth = ro (so that the absolute birth…

A: Given Data: The Birth rate rbirth=r0The death rate rdeath=r1+r2P

Q: 1. Let f: [1,6] → R be defined by f(x) = 2 + x² for 0 ≤ x ≤ 3 and f(x) = 4-x for 3< x≤ 6. Let P =…

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Q: x² - 10x 3. Consider f(x) = 9x²-x (a) Find the horizontal and vertical asymptotes of the graph of…

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Q: Ruff, Inc. makes dog food out of chicken and grain: Chicken has 10 grams of protein and 5 grams of…

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Q: 1. Write down the general form of an order three linear ordinary differential equation. 2. Find all…

A: We have to write the general form of an order 3 linear ordinary differential equations.

Q: Estimate the instantaneous rate of change in population in 2010.

A: Given: The population function for the city is Pt=1.21.05t. The variable t is the number of years…

Q: Use this definition with right endpoints to find an expression for the area under the graph of f as…

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Q: 11. Find the general solution: 1 dy 2t dt 2t = - y t²

A: Solution :  Given differential equation  12tdydt=e2t-yt2

Q: 21 Let H be the set of all vectors of the form 0 H is a subspace of R³. Show that

A: Given Data: To show that H is a subspace of R3

Q: Use the two-stage method to solve. Find x, 20, x2 2 0, and x3 20 such that X1 + X2 + 2x3 < 38 2x1 +…

A: To find- Use the two-stage method to solve. Find x1 ≥ 0, x2 ≥ 0, and x3 ≥ 0 such that x1 + x2 + 2x3…

Q: a. Express the quantified statement in an equivalent way, that is, in a way that has exactly the…

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Q: Find dy/dx using implicit differentiation: x2+5exy=10y3

A: Given that :  x2+5exy=10y3  ......... (1)  We know that  d/dx (xy) =xdy/dx +y d/dx (xn) =nxn-1

Q: Show that 2 (-r × B)² = (r² B² – (r. B)²) And, further that r² B² (r. B)² = B² (x² + y²) - If B = B₂

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Q: Sigmoid Curve:  P (c) = 1/1+e-(c - 2)  What is the independent variable? A) x B) P(c) C) c…

A: 1)Intercept is a value of y at x=0 or c=0. 2)Range is values which a function attains.

Q: Part 1: Use the graph shown to the right and the nearest-neighbor algorithm to find a Hamilton…

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Q: Let u, E C" prove that есп ū. v = v. u

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Q: Expand √10(√10-1) Write 10+√18 √2 in the form a +b√2 Expand (√5 + 1)(√5 + 2) Expand and simplify…

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Q: Compute explicitly ヌーヌ [-3] where acts on x. [Hint: Go to spherical coordinates with the origin at…

A: As per the question we are given a vector field as : (x̅ - x'̅)/|x̅ - x'̅|3 And we have to calculate…

Q: 5. a. Given that the line segment shown is 1 unit long, use the grid to lightly shade a rectangle…

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Q: Divide in binary: (a) 10001101 110 (c) 11101001010 (b) 1100000111011

A: a)  Therefore, 10001101÷110=10111.1.

Q: Find the rank of the following matrix and specify which columns are inde- pendent and which columns…

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Q: Convert to octal. Convert to hexadecimal. Then convert both of your answers to decimal, and verify…

A: (a) (111010110001.011)2 =(111 010 110 001 . 011)2 =(7261.3)8 now converting into hexadecimal…

Q: prove that Given (that means you don't need to prove it) (ÂB)¹ = B¹ ¹ (ÂÂÂÂ)¹ = ¹Ĉ† † †

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Q: 8. Use the strategy discussed in class (first and second derivative tests, critical points,…

A: Given function is: rx=x4-4x3+1 Using the first and second derivative tests, we have to find the…

Q: The following statement is false. Explain why and provide an example showing why it is false. If…

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Q: 2-2. Let X = {1,2,3}. Give a list of topologies on X such that every topology on X is homeomorphic…

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Q: Evaluate the following and show your solutions: 1. (A-B)(A + B) 2. A²+ B² 2 -21 44340 A = 4 -1 2 -1]…

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Q: The Existence and Uniqueness Theorem implies a unique solution for the initial value problem (IVP)…

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Q: Find all possible pairs (a, b) in Z3 × Z3 such that Z3[r]/(r³+ar+b) is a field.

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MATLAB

MATLAB software is a registered trademark, multi-model programming language, and numerical computing environmental system created by MathWorks. 'MATLAB' is the short-form of "Matrix Laboratory". The MATLAB software permits the utilization of matrix operations, graphical representation of data, execution of algorithms, development of user interface, and linking programs created in other languages. Even though MATLAB is developed mainly for numerical computing, there is an optional toolbox that uses a symbolic engine known as MuPAD giving access to all the symbolic computing abilities. In addition to this, a Simulink package delivers graphical multi-domain simulation and design that is model-based for embedded and dynamic systems. MATLAB users are spread worldwide across the world and use MATLAB extensively.