Seperate the variable and solve the equation 2y (dy/dx) + 2x = 0. Use the initial condition x = 0; y=2 to find the arbitrary constant C.

Q: Find the area of the region that is bounded by the given curve and lies in the specified sector. 5 r…

A: r=5θ,π2≤θ≤2π

Q: Sketch the graph of f by hand and use your sketch to find the absolute and local maximum and minimum…

A:

Q: PROBLEM No. 2. Solve the following differential equation by the method of undetermined coefficients:…

A:

Q: Find the domain of the function f(x, y) = ln(x² + y² - 9) + √-y.

A:

Q: Find the reduced echelon form of the matrix: M 1 2 3 1 4 1 2 19

A: The Matrix is given by :

Q: Find an equation of the tangent to the curve at the point corresponding to the given value of the…

A:

Q: e,f,g

A: By using previous solution sign Table xf'(x)Positive zeroNegativeDNENegativezeroPositive

Q: Evaluate the limit: limħ– →0 0-2 01/1/20 0 - 12/1/2 2 an ( 7 +h)-tan (7) h

A:

Q: 2 xy dy + 4y dx = 8 x dx 2 2

A:

Q: What values of a and b make the function f continuous everywhere? x² 4 a = f(x) = and b = - " X 2…

A:

Q: Two sets A and B are defined as follows: A = {x, y, z); B = {1, 2, 3}. Ug Oh f range of g range of h…

A:

Q: Evaluate the following integral using integration by parts. √x20 In x dx

A: I=∫x20ln⁡xdx

Q: Find the absolute maximum and minimum values of the function over the indicated interval, and…

A:

Q: √3 4 16 (x-7)(x + 9) dx

A: I=∫3416(x−7)(x+9)dx

Q: Find the slope of the tangent line to the given polar curve at the point specified by the value of…

A: The given polar curve .The aim is to find the slope of the tangent line to the polar curve at the…

Q: for the function f(x)=x^2+ x find the equation of the tangent line to f(x) at x=1 calculus

A:

Q: Roberto has plans to build a tree house in his backyard. He takes measurements from the ground and…

A: Here,

Q: 2. Consider 1, 0.1, 0.01, 0.001, 0.0001, ... (a) Write out the next three terms of this sequence.…

A:

Q: -4-3-2 VA 3 2 1-2 x = – 1 y = 1 3 4 5 x x = 2

A:

Q: Find the vertex, focus, and directrix of the parabola, and sketch its graph. (x - 6)2 = 2(y + 4) = 0…

A:

Q: Consider the following parametric curve. x = et - 4t, y = y = 8et/2, 0≤t≤ 2

A: x=et−4t,y=8et/2,0≤t≤2

Q: 2) Find the solution of the given initial value problem in explicit form. Plot the graph of the…

A: As per our guidelines we can answer only 1 question so kindly repost the remaining questions…

Q: Consider the following. Find y'(x). y'(x) = y = X = X x² +9 Find the critical numbers of y(x).…

A:

Q: For the vectors u = 37 - 8j + 2k and v=4i - 23 - 4k we have ū × v = 28i + 20j +38k. Select one: O…

A:

Q: Express each function as a composition of two functions. (Find f(x) and g(x) such that the given…

A: We have to find the given function as a composition of two functions f and g.

Q: 7. Given F(x)=√√√x+3 A. Find (fo (fog)(x) B. Find (9°F) (2) gof) → g (x) X -2 report domain and…

A: f(x)=sqrt(x+3)g(x)=x2-2.

Q: A point is moving along the graph of the given function at the rate dx/dt. Find dy/dt for the given…

A:

Q: If y = cos² 3x, then =? dy dx dy dx O dy dx dy dx = 6 cos 3x = = -2 cos 3x -6 sin(3x) cos(3x)

A: Given,

Q: 1. Use Calculus to find the absolute extrema of f(x)=3x4-4x³ -36x² +28 on the interval [-3,4].

A: By using Calculus to find the absolute extrema of  on the interval .Note: Since the student has…

Q: An exponential function f with y=f(x) has a 1-unit growth factor for y of 4. What is the function's…

A:

Q: Find dy/dx and d'y/dx, and find the slope and concavity (if possible) at the given value of the…

A: The given parametric equations

Q: The equation r³+ y³ = 3ry defines a curve named as the Folium of Descartes. (a) Use implicit…

A: The equation  defines a curve named as the Folium of Descartes.By using implicit differentiation to…

Q: 5 Determine the difference quotient for the function f(x) = 2x-1.

A:

Q: The magnitude of the vector (3, -2, 4) is 29. Select one: O True O False

A: The given statement "The magnitude of the vector  is "

Q: Find the square root of 7225 with the modern method

A: A number's square root is a value that, when multiplied by itself, returns the original number.

Q: 2. a. C. Determine the critical number(s) for the following functions. f(x) = 17-6x + 12x²…

A:

Q: Find a formula for the nth term of the sequence where an is calculated directly from the value of n.…

A:

Q: 7. 8. 9. sect cos t sect 1+sec²x tan*x+1 sin t csc t = sin t = cos x + 1 cos t sect = 1

A: Given.

Q: (a) Find and sketch the domain of the function f(x,y)=√x+2+√√y+3

A: To find and to sketch the domain of the following function.Note: Since the student has posted…

Q: Find the direction cosines and angles of u and show that cos²a + cos² ß + cos² y = 1. (Round your…

A:

Q: The limit represents f '(c) for a function f(x) and a number c. Find f(x) and c. [9 3(1 + Ax)] - 6…

A: limΔx→0[9−3(1+Δx)]−6Δx

Q: 2. by (No need to justify for full credits if your choice is correct.) A. B. C. Which of the…

A:

Q: 1. x dy dx – 4у = х6 ex 9x

A:

Q: Suppose f(x, y) = x² + y² - 8x and D is the closed triangular region with vertices (8,0), (0,8), and…

A:

Q: Solve the given initial-value problem. y(x) = 2y" + 3y - 2y = 10x² - 4x 13, y(0) = 0, y'(0) = 0 -

A: Since you have asked multiple questions in a single request so we will be answering only first…

Q: Solve the given initial-value problem. Y(x) = y" + 4y' + 5y = 35e-4x, y(0) = -5, y'(0) = 1

A: y'(0)=1

Q: 1. Solve dy_3-x-y x + y €1 dx 11

A:

Q: Use Lagrange multipliers to find the minimum value of the function f(x, y) =x² + y² subject to the…

A:

Q: For what values of a and b does lim x→0 a = b = sin (2x) x³ +a+ b 2/2) = x² = 0?

A:

Q: Find an equation of the tangent line to the curve at each given point. x=2-3 cos 6, y = 3 + 2 sin 8…

A: