Which of the following are separable differential equations? A. y = 2x - 3y +1 B.(4)=x+y □ C. 2xydx + (x² − 1)dy = 0 - OD. = 172²2 0 | - dy dr dy E. dy OF. = xy dz x+x²y=x dr dy dr G. = x + y² OH. dy + yx² = x² dr

Q: Consider polar curves C1: r = 3+2sine and C2: r = 8sin0 1. Find the Cartesian equation of the…

A:

Q: Evaluate the integral. (Use C for the constant of integration.) [7. 7z³e² dz

A: ∫7z3ezdz

Q: Q1: Solve the following equations system, using Gauss elimination method 4y1 + 2y2 +3y3-5 =6 3y₁ +…

A: We need to solve the given system of equations using the gauss elemination method which uses the row…

Q: Determine if Rolle's Theorem and the Mean Value Theorem is applicable on the specified interval. If…

A: Condition to apply Rolle's Theorem and Mean value Theorem 1. Function must be continuous over…

Q: a) lim (-2x¹) = 8118 ) lim (-2x¹) = xx ) lim -√x = 118

A:

Q: Let a = (0, 1) and b = (4, -4). Show that there are scalars s and t so that sa + tb = (16, −17) You…

A: We have, a = ⟨ 0, 1 ⟩  b = ⟨ 4 , -4 ⟩ sa + tb =⟨ 16 , -17 ⟩

Q: (a) Differentiate the following functions with respect to t: (i) (ii) y = 4t-t² t-1 y = esint 2+2.5…

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

Q: Second derivative of f(x) =2^x/x

A: To find the second derivative of the following function. fx=2xx

Q: Find a plane containing the point (-2,-1,2) and the line of intersection of the planes -3x + 5y + 8z…

A:

Q: Find a polynomial f(x) with leading coefficient 1 such that the equation f(x) = 0 has the given…

A: Given: Polynomial f(x) has a leading coefficient of 1, has a degree of 7 andhas roots 4,5,3-i and…

Q: Construct a problem where you have to find the inflection point that is equal to 1/2.

A:

Q: Use differentials to estimate the amount of metal (in cm³) in a closed cylindrical can that is 18 cm…

A:

Q: Evaluate the following integral S 4x cos (5x) dx=

A:

Q: A waste management company is designing a rectangular construction dumpster that will be twice as…

A:

Q: differentiate the function f(v)=(v^1/3-2ve^v)/v

A: fv=v13-2vevv NOTE:-Here in question brackets are not given v^1/3 but as we see it must be v^(1/3)…

Q: The integral [7 sin 7 sin(x) cos(x) dx can be evaluated in four different ways: (1) The substitution…

A: let H=∫7sin(x)cos(x)dx

Q: Evaluate the indefinite integral. (Use C for the constant of integration.) [ sin (√x) dx

A: Given integral is ∫sinxx dx

Q: Find all the second partial derivatives. f(x, y) = xy - 4x5y² fxx(x, y) = fxy(x, y) fyx(x, y) = =…

A:

Q: Find a quadratic equation with the given roots. Write your answers in the form Ax2 + Bx + C = 0.…

A:

Q: Solve 4x cos(3x) dx using Integration by Parts

A:

Q: 8 2k Σ k=1 k!

A:

Q: Find the volume of the solid that lies below the paraboloid using Double integrals in Polar…

A: This is question of calculus Here we have to find volume using double integration method  Curve…

Q: D. MEAN-VALUE THEOREM & ROLLE'S THEOREM Determine if Rolle's Theorem and the Mean Value Theorem is…

A: Note:- Since you asked multiple question , according to our policy we can solve only first question…

Q: For the angle 0, find the following. (a) tan (0) (b) cot(0) (c) sec(0) (d) csc(0) 37 (-12,-35) y 0

A: Figure

Q: The revenue, in dollars, derived from the sale of a units of device model SDP732 is given by…

A:

Q: 6. Given u = a. 5u b. u. V c. [2, -5]and = [-7,2] find

A: Given: v→=-7, 2 To find: v→ Note: Since, the student has mentioned to solve only question 6(c), so…

Q: Determine whether the three points P = (-3, 7, 1), Q = (-2,9, 4), R = (-1, 12, 7) are collinear by…

A: To determine whether the points P=-3, 7, 1, Q=-2, 9, 4, and R=-1, 12, 7 are collinear by computing…

Q: Express the given product as a sum containing only sines and cosines. 170 2 sin COS 0 A THE CHOICES…

A:

Q: 1. 2. Find f'(x) and f"(x). Determine the following Domain a. b. x and y intercepts t. The critical…

A: derivative calculated by differentiation with respect to x

Q: Solve the given differential equation by separation of variables. (ex + 1)²e-y dx + (ex + 1)¹e-x dy…

A: We need to solve (e^y+1)^2 e^(-y)dx+(e^x+1)^4 e^(-x) dy=0.

Q: 19. an - (₂)

A:

Q: Determine whether the three points P = (-5, -4,-3), Q = (-8,-10, -12), R = (-11, -15, -21) are…

A:

Q: 3) Refer to the information in Problem 2. Find the distance traveled by the object for the interval…

A: We have, Vertical position:    y(t) = 32t - 8t2  Interval:  0 ≤ t ≤ 3

Q: In this problem, y=c₁ex + c₂e-x is a two-parameter family of solutions of the second-order DE y" - y…

A: Given that ,   y = c1ex + c2e-x  is  a solution of the differential equation y''-y =0. We have to…

Q: Find a quadratic equation with rational coefficients, one of whose roots is the given number. Write…

A: we have given rational root =12+174

Q: Find the volume of the solid in R³ bounded by y = x², x = y², z = x+y+9, and z = 0. V =

A: I am going to solve the problem by using some simple calculus to get the required result of the…

Q: Find the first partial derivatives of the function. f(x, y) = x³ + 6xy7 fx(x, y) fy(x, y) 11

A:

Q: Find the direction in which the maximum rate of change occurs for the function f(x, y) = 3x sin(xy)…

A: To find:  the Direction in which the maximum rate of change occurs for f(x,y)=3xsin(xy) at point…

Q: Jhy Find following limits if they exist. Enter DNE if the limit does not exist. g(x) a h(x) g(x) 4.…

A: Note : As per our Guidelines , we can solve first three subparts . Please repost remaining parts.

Q: Find the most general antiderivative of the function. (Check your answer by differentiation. Use C…

A:

Q: ly the Ratio Test to determine convergence or divergence, or state that the lim n→∞ an+1 an n n² + 1…

A:

Q: y = 1/(x² + c) is a one-parameter family of solutions of the first-order DE y' + 2xy² = 0. Find a…

A: y=1x2+c is a one parameter family solution of differential equation:  y'+2xy2=0.Initial condition…

Q: Find the following for p =, q =, and r = Find 8r+ 3q Answer: ^ Submit Answer

A: p=-7, -6q=-1, -11 andr=0, 9

Q: 3) Factor the following polynomials: (a) 12x²y + 4xy² - 18ay (c) 2x² - 9x - 18 (d) 27y³ - 125 (b) d…

A: Given polynomials are : (a) 12x²y+4xy²-18xy ;  (b) d²-5d-66 (c) 2x²- 9x - 18 (d) 27y³-125 (e) 121x²…

Q: 8) A region is bounded in the second quadrant by the curve y = In(1-x), the line y = 3, and the…

A:

Q: Let F(x, y, z) = xi + yj + zk. Evaluate the integral of F along each of the following paths. (a)…

A:

Q: Use integration by parts to find the integral. (Use C for the constant of integration.) [x²1 x…

A: I=∫xnlnaxdxusing integration by parts, taking u=lnax  and…

Q: Let F(x, y, z) = (P(x, y, z), Q(x, y, z), R(x, y, z)) = (y cos(x) — y, sin x +2yz − x, y² + 1) be a…

A: To show that the vector field F = (P, Q, R) is conservative, we need to demonstrate that its curl is…

Q: The light bracket ABC is freely hinged at A and is constrained by the fixed pin in the smooth slot…

A: To determine the value of the resistance force in this situation, the equilibrium conditions must be…

Q: Use the chain rule to find dw dt dw dt W = In (√x² + y² + z²), x = 9 sin(t), y = 8 cos(t), z = 5…

A: W=lnx2+y2+z2 x=9 sin(t) y=8 cos(t) z=5 tan(t)