Solve the initial value problem 11 -x dx - y = ¹²e³; y(0) = -1 dx 8 Find the general solution ● (x² + 1) dy x + 3xy = 6x dx

Q: The left, right, trapezoidal, and midpoint rule approximations were used to estimate =1²₁ f(x) dx,…

A:

Q: Graph the functions on the interval [-7,7]. Include all asymptotes and labels on your graphs where…

A: We have to plot the graph of 1) y= sin x 2) y = cos x 3) y= tan x Under the given interval with…

Q: Because of the rainy season, the depth in a pond increases 3% each week. Before the rainy season…

A: given that, weekly increment= 3%  initial depth= 10 feet what is the equation that best represents…

Q: ider the following. f(x) = 1 x+2 (a) State the domain of the function. all real numbers x all real…

A: Given query is to find characteristics of the function.

Q: (b) y'' – 4y' + 4y = 3e2x

A:

Q: Determine the area bounded by x = -y² + 10 and x =(y-2)²

A: Given curve :x=-y2+10x=y-22

Q: If a parametrized curve is given by: r⃗ (t)=⟨2t^3,10ln(t),5t^2+9t⟩ At t==2, the position vector is…

A:

Q: x-1, if x ≤-2 f(x)=2x-1, if -2 4

A: Use bigger dots for equality

Q: Find the domain and range of the relation Provide your answer below: domain: range: {(0, -3), (-7,…

A:

Q: 6. Area of a Region between Two Curves. a. Determine the area of the region bounded by f(x) = (x −…

A: Since the student has posted multiple questions and does not mention any specific question, so we…

Q: Solve the inexact differential equation ydx + (2xy-e-2y) dy = 0.

A:

Q: Solve the inexact differential equation y dx + (2xy-e-2) dy = 0.

A: The given differential equation is; ydx+(2xy-e-2y)dy=0

Q: 2. Find the solution of the given initial value problem. y" — 6y' +9y = 0, y(0) = 1, y'(0) = 2.

A:

Q: Which of the following is the general solution of xln x + y = ln x² ? dx y = lnx + C y = ln x + In x…

A: Option "B" is correct

Q: Determine if the function below is even, odd, or neither. Select the correct answer below: even odd…

A:

Q: The graph of a derivative f' is shown to the right. Use the information in the graph to determine…

A: To find the intervals where function is increasing or decreasing.

Q: Which of the following functions has a graph that is thegraph of y = 2x shifted down 3 units?(a) y =…

A:

Q: A tank initially contains 100 liters of pure water. A brine solution con- taining 2 kilograms of…

A: We have to find the time at which concentration= 1/5 kg

Q: 3s +4 F(s) = s(s± + 6s +13) 2

A: Explanation of the answer is as follows

Q: 3 tan ³x dx

A: Given:      ∫tan3x dx Rewrite:     =∫tan2xtanx dx    we know that         tan2x=sec2x-1…

Q: Find the critical numbers of the function. (Enter your answers as a comma-separated list.) h(x) =…

A: The given function is h(x)=sin2x+cosx   ,  0<x<2π We have to find the critical numbers of the…

Q: c) f t√t + 4 dt e) S X 25+16x² dx 25+16x² d) f 25 dx x (19wansoy dilquma) dx 25+16x² f) S

A:

Q: Verify that and use this equation to evaluate 2-1(2-4) (Aª dx 1

A:

Q: Question 6. Find an equation for the surface consisting of all points P that are equidistant from…

A: See this solution in below.

Q: 3. An object is thrown vertically upwards with an initial velocity 20 ms ¹. The rate of displacement…

A:

Q: Find the partial fraction decomposition of -6x - 16 x² + 6x + 8

A: -6x-16x2+6x+8

Q: A B The integrating factor for (2y – xy²)dx − (3x + x²y)dy = 0 is 2xy 1 5xy

A: The given equation is; (2y-xy2)dx-(3x+x2y)=0.

Q: An aquarium 6 ft long, 3 ft wide, and 2 ft deep is full of water. (Recall that the weight density of…

A:

Q: QUESTION 4 Evaluate Stan²3x de 01 3" 01 tan3x -x +C 01 tan³3x + C tan³3x+C O tan3x - x +C

A:

Q: Evaluate lim (x,y,z)→(π,0,3) ze -2y cos(2x)

A:

Q: Find the following derivative and state a corresponding integration formula. 3x - 1 2x2 + 2x + 2 d…

A: Derivative

Q: 2. The path taken by a particle is a horizontal line as it moves according to the law 3 s = ²²…

A: Concept: Velocity is the rate of change of displacement that is  v(t)=ds(t)dt Acceleration is the…

Q: (4) Find the area between y = 2 sin x, y sin 2x, x = 0, and x T. Sketch the region.

A:

Q: 5. Approximate Ay using differentials for y = x² - 4x at x = 6 when Ax = dx = 0.03.

A:

Q: h (x) = x² lnx, at

A: Topic:- function and it's derivative

Q: 2) Is the discontinuity x = 0 for the function f removeable or non removeable. Fully justify your…

A: We need to explain removable or non removable continuity at x=0.

Q: r(t) = (t, ln(t), 0)

A: Given rt=t, lnt, 0

Q: Find the absolute extrema of the function on the closed interval. minimum y = 7 cos(x), maximum…

A:

Q: In the US the voltage in the electrical wiring of a typical home is given by V(t) = 170 sin(120nt).…

A:

Q: 3. The Area of A Plane Region a. Find the upper and lower sums for the region bounded by the graph…

A: Concept: According to the limit definition: A=limn→∞∑i=1nfa+i(b-a)nb-an Here A is the area According…

Q: d. e. Σ(**) - η 4k Τύπος (Σ(44)) - lim η-400 η k=1 - A C

A:

Q: Consider the differential equation x +T=e* with 7(0) = 1. What is the approximate value dx of T(2)?

A: Given, xdTdx+T=ex with T0=1 We have to find the approximate value of T(2).

Q: If the amount of capital that a company has at time t is f(t), then the derivative, f'(t) is called…

A:

Q: Find the absolute minimum value of the function f(z) shown below. 1 00 7 S 3 2 1 0 0 1 2 3 4 5 6 8

A: We need to find out the absolute minimum value.

Q: In Exercises. the region. 37. 3 2 ), use an iterated integral to fi y=4-x² X

A: Topic:- Calculus

Q: Find particular solution of the differential equation in the attached  image

A:

Q: Given h(x, y, z) = 5 x² + 2²-1 7 determine all points at which h is continuous.

A: We have to find the all continuity point from the given information

Q: tangent

A:

Q: Analyze the situation. Identify a reasonable domain and range for the situation. The revenue earned…

A: Here we have to analyse the given situation and find the domain and range of it.

Q: dx 2. Evaluate the improper integral S Why is it an improper integral? (x − 1)² 3. Find the arc…

A: