can someone explain how he gets the partial derivative done here. i dont understand the process

Q: f(t) = t, 0 st < 1 1, t2 1

A: Given function is f(t) = t,0≤t&lt;11,t≥1

Q: Which of the following is a power series representation of ƒ(x) = ln x, x ≥ 0? (Hint:In x = /dx) a.…

A: f(x)=lnx We know Taylor's series expansion of f(x) about x=a is…

Q: Determine whether (p+q)^r is equivalent to p(q^r). To get full credit on this question, you must…

A: We have to use truth table to find statements are equivalent or not by using following outcome…

Q: 1. Construct the intersection for the collection of sets: A₁ = (0,2,4,6,8) A₂ = [0, 1, 2, 3, 4) A3 =…

A: I do both 1 and 2 questions. In second question if matrix is symmetrical than we will find…

Q: Use a Taylor series centered at r= 1 to approximate the value of the integral farctan(x) dx accurate…

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Q: Use the method of variation of parameters to find a particular solution of the differential equation…

A: Given differential equation 4y''-4y'+y=80et/2 which can be written as  y''-y'+14y=20et/2=f(t)

Q: 3. 4. [ DETAILS Verify Green's Theorem by evaluating both integrals ам [ 04 - [ / (²²²_-2/7) (ON dA…

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Q: Determine the median of the following data set: 51, 29, 94, 77, 50, 77, 76, 10, 39

A:

Q: Consider the diagram below in a two dimensional Cartesian x-y plane. The parabola is given by the…

A: we will use symmetry of given figure about y-axis and condition of quadratic equation to find…

Q: Consider the points P(1,0,3) and Q(5, 2, -1), and the line 1: { x = -7-2t y=t z = 9+t

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Q: Note: Show all your calculations steps. A 14-m beam is subjected to a load, the shear force follows…

A: Given: The linear shear force is given by: Vx=5+0.25x, The bending moment is given by: M=M0+∫0xVdx…

Q: Show that Y=22.4sin(1.1x) is an eigenfunction of the operator (d²/dx²). What is the eigenvalue? O O…

A: Here we have given that Y=22.4sin1.1x is an eigen function of the operator d2dx2. So, we have,…

Q: Consider the function f(x, y) - 20²-11y2 + 10zy over the unit square 0≤x≤ 1,0 ≤ y ≤ 1. NOTE: Enter…

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

Q: If csc(z) = Give exact answers. sin (1) = cos()-[ = 28 3 tan()-[ = (in Quadrant 3), find

A:

Q: Use greedy algorithm (starting point A) and edge picking algotrithm to find the minimum weight.

A: We have been given a weighted connected graph. We have to find the minimum weight using the greedy…

Q: Solve: x"-x+ 5 y'=t y" - 4 y-2 x' = -2 with x(0) = y(0) = x'(0) = y'(0) = 0 Let L{x(t)} = U(s) &…

A: Solution:

Q: 5. a) Given the weighted graph: 2 2 X 2 3 3 1 3 3 Find a minimal spanning tree for the weighted…

A: As per our company guidelines we are supposed to solve 1st question. Kindly post the other in next.

Q: Approximate the definite integral using the Trapezoidal Rule and Simpson's Rule with n = 4. Compare…

A: given function ∫1221+x2dx using trapezoidal rule with n=4 let fx=21+x2 h=b-an substitute the values…

Q: dN₁ dt dN₂ dt 5N₁ 1 N₁ 20 N₂ 17 9N₂ 1-- N₂ 20 N₁ 17 1.6- 0.6-

A: This is a question of the equlibrium of the system.

Q: Correct. If y, and y₂ are linearly independent solutions of ty" + 4y + tey = 0 and if W(y₁, y₂)(1) =…

A:

Q: Determine whether the equation is exact. If it is exact, find the solution. 3 2 2eycosy+2 = C…

A:

Q: 1. Consider the curve C = C₁ UC₂, where C₁ is the line segment from (0, 1.1) to (1,1,0) and C₂ is…

A: Given Data: The given curve is C=C1∪C2, where C1 is the line segment from 0,1,1 to 1,1,0 and C2 is…

Q: Use the definition of the Laplace transform to find L{f(t)}. (Enter your answer in terms of s.)…

A: The given problem is to find the Laplace transform of the given unit step function.

Q: ay Write down a differential equation of the form =ay + b whose dt 11 12 solutions all approach y =…

A: Given That  differential equation  y'=ay+by=1112 when t→∞ To find : the differential equation the…

Q: Solve the following equations. TU cot ¹(1-x) - tan¹(x) = 4

A:

Q: 1. How much would the equal monthly payments be on a student loan of $10,500 that has a ten-year…

A: You mentioned only 1 and option A to solve, I will solve both of them but if you want I will solve…

Q: OED={(u, v) R²u0, v0}

A:

Q: Theorem: if I is a Positive implicative Bck-algebra Then (Lx),,Lo) is a BCK-algebra

A: Consider the given theorem, '' if X is positive implicative Bck-algebra then Lx,⊙,L0 is a…

Q: Suppose T:R³ R³ is the transformation induced by the following matrix A. Determine whether T is…

A:

Q: (b) (2 + 3i)¹+i

A:

Q: Produce an example of an element of Co (R, R) which is not an element of the following vector…

A: Correct answer is f(x)= Sin(x) which is infinitely many times continuously differentiable but it is…

Q: The figure to the right shows the letter L in a rectangular coordinate system. The figure can be…

A:

Q: (10) Write a summary (unit frame, scale factors, gradient, arc length, volume element, and…

A:

Q: y' = 133 110 -1 1 2 y: X = 2, 1, 1

A:

Q: VIII. Evaluate the following definite integrals. (a) ₁²√³-5da

A:

Q: 10. The ratio as n gets larger is aid to approach the Golden ratio, which is approximately equal to…

A: When n gets larger, the ratio is =5+12~1.618 The inverse of this ratio is =25+1

Q: Find the value of the constant k so that the differential equation (6xy³ + cos y)dx + (kx²y² − x sin…

A: For the given Exact Differential (6xy3+cosy)dx+(kx2y2-xsiny)dy=0 value of k is 9 Hence option (A) is…

Q: 28. Consider the initial value problem y+y=1-t, y(0) = yo. Find the value of yo for which the…

A: Consider the initial value problem y'+43y=1-14t, y0=y0   To Find: The value of y0 for which the…

Q: 5. Let S be the negatively oriented surface defined by R(u, v) = (u², v², uv), where (u, v) = [0, 1]…

A: Given :             R→u ,v =u2 , v2  ,uvF→x , y ,z =z, z , xy To Find : ∫02∫01F→.Ru→×Rv→du dv

Q: Answer true or false. F(s) = s²/(s² + 4) is not the Laplace transform of a function that is…

A: Properties of Laplace transformation. L-11=δ(t)L-1as2+a2=sinatL-1aF(s)+bG(s)=aL-1F(s)+bL-1G(s)

Q: 2 H√√x dy with initial value problem y(4) 2 cos Y dx = TT 4

A:

Q: 4. Let S be the triangular region in R3 with vertices at (2,0,0), (0,6,0), and (0, 0, 3) with upward…

A: Given: Let us consider the given, surface S with vertices, 2,0,0,0,6,0, and 0,0,3 Let's determine,…

Q: Fill in the blank. (Enter your answer in terms of t.) 1 { } L25² + 22 رسید

A:

Q: dy Write down a differential equation of the form = ay + b whose dt all other solutions diverge from…

A: Hint: Assume the first order differential equation in the given form so that when t→∞ then solution…

Q: Find the possible values of a and b in the expression u(x, t) = cos (at) sin (bx) such that it…

A: To Find: All those values of a and b such that u(x,t)=cos (at) sin (bx) satisfies the wave equation.

Q: a) z=4x²-9x²y+2y³, com x=2 sen(t) e y=cos (t); b) w=xe, com x=4t², y=5e²¹ e z=2t². c) z=x y²+2x²,…

A: Introduction: When the independent variables of a function is again dependent on a single parameter,…

Q: Find the general solution of the differential equation y" + 5y14y=-62t + 28t². NOTE: Use t as the…

A:

Q: max f(x, y, z) = -xz-x² + y-yz - y² - 3z² x,y,z ...5] Express V f(x, y, z) = 0 in the form Ax = b…

A:

Q: x²y" - xy + xy = 0, y(1) = 0, y (L) = 0, L > 1

A: As per the question we are given a second order linear differential equation as : x2y'' - xy' + λy…

Q: Express the following function in terms of unit step function and hence find their Laplace…

A: