Solve each equation by extracting the square roots. 1.x² = -31 2. (x6)² - 7 = 0

Q: (2xy-3x²) dx + (x ² + 2y) dy = 0

A: As we know that; The differential equation Mdx+Ndy=0 is said to be exact, if ∂M∂y=∂N∂x. The solution…

Q: Let g(x, y) = sin(8x + 2y). 1. Evaluate g(1, -2). Answer: g(1, -2) = sin(4)

A: Given function g(x,y)=sin(8x+2y)

Q: Q1) Solve the following system of algebraic equations using matrix inverse method. 6 10-0

A:

Q: 1. Find y' of tan(x²y) = 3x + y²

A: Given:      tanx2y4=3x+y2 differentiating on both sides   ddxtanx2y4=ddx3x+y2  Applying…

Q: Draw the region of integration and reverse the order of integration to So evaluate the integral. 0 1…

A:

Q: the limit is positive or negative infinity. If the limit does not exist as a finite number or as…

A:

Q: f(x,y)=(5x°-4y3, + 4xy²

A:

Q: ph are given. y 2 -4 -6 2 4 X

A:

Q: find the gradient of z = x² + y² - 3x4 at point (2, 1)

A:

Q: III. WITHOUT SOLVING the given problem, DEFINE the variables and unknown quantities, and SET-UP ONLY…

A: We have given a vacation house is rented.  Let,  x represents numbers of days C(x) represents cost…

Q: Use the tabular method and the properties of limit to find the limit lim ex-4 X-4

A:

Q: Solve dy dr 3y-1x Er

A:

Q: Find the derivative of the function. y=2xe-3x −3ex4 dy dx ||

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

Q: Q4/ The region between the curve y=√x, 0≤x≤4, and the x-axis is revolved about the x-axis to…

A: We need to find volume.

Q: The daily cost per unit of producing a product by the Ace Company is 35+ 0.2x dollars and the price…

A: To find out the revenue function, cost function, profit function, marginal profit.

Q: 2. Obtain the general solution using separation of variables. dz = a(cos 0 dz + z sin 0 de)

A:

Q: 10.) Find the simplified form of the difference quotient. f(x)=x² + x

A:

Q: angle between 0∘0∘ and 360∘360∘ that is coterminal with the 1950∘1950∘ angle is what degrees.

A: Topic:- trigonometry

Q: Given f(x, y, z) = x²y³z - 3xy²z³ + 5x²z - y³z, find fxyz

A:

Q: z = x² + x - 3xy + y3 - 5, find all points (x, y) wherein zand zy = 0.

A: The points are (1/4,1/2) and (1,1) the detailed solution is given below

Q: - Find and sketch the domain of the functions: √x+y+1 x-1 b) f(x, y) = x ln(y² - x) c) f(x, y) =…

A: The given functions, a) fx,y=x+y+1x-1b) fx,y=xlny2-xc) fx,y=6-3x-2y We have to find the domain of…

Q: 1. For each of the functions f(x, y) below, describe its domain in set notation, give a geometric…

A: Dear student  We are allowed to solve the first 3 subparts of the question. If you need the rest of…

Q: Find an equation of the line that passes through the point (-1, -2) and is perpendicular to the line…

A: Let's find equation of line.

Q: 2. Consider the equation du = -0.5y²(y² + 1)(y² − 4)(y + 1)esin y (a) Find all equilibrium…

A: To find the equilibrium solution of the differential equation , set the differential equation to…

Q: (b) dy 3-4012 4xy + by2 ; dz = (1) y(1) = -1

A:

Q: for the function f(x) = 7X+9 and (exact answers) find the following 1. f(g(x)) = 2₁ g (f(x)) = 3.…

A:

Q: 1. Determine the domain and range of f(x) = 5

A: The domain of the polynomial function, fx=a0+a1x+a2x2+....+anxn is always a real number. Where n∈N…

Q: Complete the table and predict the limit, if it exists. (Round your answers to three decimal places.…

A: Let's find limit is exit or not.

Q: 20. 8] n=1 2² 5n+10

A: D'Alembert Test: Let ∑n=1∞un be a series such that, limn→∞un+1un<1 Then this series is…

Q: Find the general solution of each of the following. J.. 1 1. in 2. y tan² x dx + In¹y dy = 0 000² v…

A: Please see the below picture for detailed solution.

Q: At which value of y does the relative minimum for the curve y = 3x³ 3x² - 24x + 10. A. -19.5 B. -26…

A:

Q: Find for x³ + y²x-3 = 0 dy dx

A:

Q: Use the given graph of f to find a number & such that if |x-1| < 8 then [f(x) - 1|< 0.2. 8 = 1.2 y 1…

A:

Q: 1 A used piece of rental equipment has 5 years of useful life remaining. When rented, the equipment…

A: A piece of rental equipment has 5.4 years of life remaining When rented,the equipment brings in $600…

Q: 2ly² - 4y + 5x = 21 FIND Y'

A:

Q: Use the theorem given below to find the curvature of r(t) = tj + tk. k(t) = Theorem: The curvature…

A:

Q: 2. Divide 20 into two parts. Find the two positive numbers if: (a) their product is a maximum; (b)…

A:

Q: Suppose that the weekly sales volume y (in thousands of units sold) depends on the price per unit…

A: We have to find the value of derivative at $21 and interpret the answer.

Q: . Determine the W3 fourth root of 16+16i in exponential form. COMPLETE THE MISSING THE BLANKS FOR…

A:

Q: Find the general solution of the Differential Equation dy dx 4y x(y-3)

A:

Q: G(x)= x³ +3x+2 x+2 [[x]] + 1 -1-x-21 - 4 x+3 + 1 x-r if x<-1 if -1 ≤ x 1 if xz1

A:

Q: 2. Let us consider the given statement ~p ^ ~q The truth table of the statement is PT T LL FL q T F…

A: We have to write the final result of the table in words that too in a simple way to understand.

Q: 0:0(0-¥x)+XP(46+2)

A:

Q: (dy/dx) + 2y = sin2x First-class homogeneous DE Second degree homogeneous O DE second order DE…

A: Given differential equation has function of x only on right hand side.  So, it is heterogeneous…

Q: The price per barrel of crude oil in the period 1980-2013, in constant 2014 dollars, can be…

A: Topic- functions and derivatives We are given,Price per barrel of crude oil since t years of the…

Q: Q1/ Find of the following functions dx 1) y=²-1 and x=21+3

A:

Q: Solve for the complete solution of the differential equa y" − 6y' + 9y = 0; y(0) = − 1, y'(0) = 2.…

A: Topic:- differential equations

Q: 23 Using the Table method, find the limit. Make sure you show all steps 4x +9 x+2 lim, g(x)

A:

Q: Find the general solution of each of the following. rdp-(p+√pr)dr=0

A: Our Aim is to find the general solution of the following given below:-rdp-p+prdr=0 -(i)

Q: 1. In each of the following initial value problems, determine the maximal interval in which the…

A: