Show that dri dt = r2 dr2 r₁ dt. If r₁(t) = t², what is when A₁ = 4A₂? dr2 dt

Q: Given f(x, y) = -5x¹ − 3xy² + 4yº, find fz(x, y) = fy(x, y) -

A: We have .Now, we need to find f_x(x, y) and f_y(x, y).

Q: 1. у ул y=3x - x² 0 y=x (2, 2) AX

A:

Q: if f(x)= xe^x, determine f^(400) (x)

A: To determine the 400th derivative of the function f(x) = xe^x, we can follow a systematic approach…

Q: Assuming that the equation below defines y as a differentiable function of x, find the value of…

A: Using differentiation

Q: The plane x + y + 2z = 10 intersects the paraboloid z = x² + y² in an ellipse. Find the points on…

A:

Q: During the month of January, "ABC Appliances" sold 49 microwaves, 16 refrigerators and 27 stoves,…

A: Given:We are required to find:

Q: If f(x) = x²/(1+x), find f "(2). f"(2) =

A: Use the quotient rules of the derivative

Q: What is the exact value of a trigonometric function of a given angle? Select True or False for each…

A:

Q: Suppose an airplane is flying 170 mph with a heading 25° east of south (295° measured…

A:

Q: Write the following expression Ohm--h(m+3) O In (m) - In (m + 3) 2 In (m) - In (m+3) hm+=h(m+3) m as…

A: To write the following expression as a  sum and/or difference of logarithms without exponents.

Q: 2. Determine the Cartesian equation of the plane containing these lines: z+2 x-5 z+5 3 and L₂: *5 =…

A:

Q: Suppose that the mass in a mass-spring-dashpot system with m = 20, c = 9 and k = 1 is set in motion…

A:

Q: What is the area of the region bounded to the right by = by x = y²? 543-2-1 2 3 4 5 O co/ co/ col∞o…

A:

Q: For the functions w = 2x² + 3y², x= cost, and y = sint, express terms of t and differentiating…

A:

Q: Find parametric equations for the line tangent to the curve of intersection of the surfaces at the…

A:

Q: If f(x) = 3x-2 and g(x)=x+1, then (f(g))-¹(a) equals 01-2 O (3-1) O x-1

A:

Q: (iii) Consider the function C(Q₁, Q₂)=Q-30102+Q2. What level of Q₁ and Q₂ locally minimise this…

A: According to our guidelines , we can answer only first question (due to multiple questions). Kindly…

Q: Factor the following expression by grouping.   x3−2x2+3x−6

A: let

Q: Find the equation for (a) the tangent plane and (b) the normal line at the point Po(4,0,4) on the…

A:

Q: Find the derivative of the function at Po in the direction of A f(x,y) = - 4xy-4y², Po(-5,4), A=…

A: Given :- The function To Find :- The derivative of the function at P0  in the direction of A.

Q: 4. x-6 3 a) Determine the point of intersection of the two lines. b) Determine the acute angle…

A:

Q: 9. Given f(x) = x³ - 5x and its derivative f'(x) = 3x² - 5, find the equation of the tangent line to…

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

Q: Let g(x)=3x²-6x-5 Find a. g (-2) | b. g(0) c. g(-3a)

A:

Q: tan (sin ¹(-)) cos (tan ¹(1)) Enter your answer, as a simplified fraction, in the box. What is the…

A: let

Q: What are the solutions of the equation cscx tan x = 2√3 Drag all correct solutions to the box to…

A:

Q: 2 Find the volume of the region bounded above by the paraboloid z = x² + y² below by the triangle…

A:

Q: 7) Find the Taylor series generated by fat x = 1 f(x) = 2x³ + x² + 3x - 8 8) Find the Taylor series…

A:

Q: Find the gradient of the function f(x,y)=√2x+3y at the point (-1,2). Then sketch the gradient…

A:

Q: 5. Which equation can be solved by referencing the graph below? -1/2 -11/4 3 cosx – 1 = sinx O…

A: The range of both cosine and sine function is .The value of the sine function is zero for all…

Q: Find the domain of the following function. g(x,y)= In (x²-y)

A:

Q: Solve the following autonomous differential equation with the given initial condition. dy dt =…

A:

Q: Use the Chain Rule to find dt where z = x cos y, x=t, and y = 6t²

A:

Q: Find all the second-order partial derivatives of the following function. w=5ye3x² - 4y

A: w= 5ye3x^2-4yWr have to find all second order partial derivatives

Q: Q7. If a beam of light that has intensity k is projected vertically downwards into water, its…

A: If a beam of light that has intensity k is projected vertically downwards into the water its…

Q: Find the volume of the solid obtained by rotating the region bounded by the given curve about the…

A:

Q: What is the maximum value of for 0≤x≤ 10? 2e - 1

A:

Q: From first principles (that is, using the formal definitions of convergence and divergence) show…

A:

Q: Find the Volume V(S) of the solid S generated by given R: R is the region bounded by -x²+9 and…

A:

Q: 1. Simplify first, then evaluate. Do not use calculator. a) logg 6-logg 3 +logs 2 b) log, 3√3

A:

Q: Let f(x, y) = x² + 2y¹ - 40xy

A:

Q: Which of the following graphs is consistent with the differential equation dx = x y

A:

Q: Write the row vectors and the column vectors of the matrix.   0 −3   −2 1 (a) the row vectors…

A: I have appended the concept used in the solution procedure part

Q: Q8. The concentration of a certain prescription drug in the bloodstream after a single dose is…

A:

Q: Find the volume of the solid generated by revolving the region bounded by the graphs of the…

A:

Q: Write the following in exponential form: y = ln(25): O e25 = y O (25)e=y O ev = 25 O (25) = e

A:

Q: f(x) = = Find (fog)(x). Find the domain of (f o g)(x). (Enter your answer using interval notation.)…

A:

Q: Let f(x, y) x + 4y 2¹+4 I Evaluate f(0, 1)

A:

Q: The population of rabbits in a controlled system can be described by P(x) = x² + 18x + 19, where x…

A:

Q: Using the Washer Method, compute the volume of the solid of revolution generated by revolving the…

A:

Q: Replace R₂ by (-8)R₁ + R₂. 14-8-7 84 7 8 -5 1 5 2 (-8)R₁ + R₂ = (-8)R₁ + R₂

A: