Suppose f(x,y)=x3y. At the point (1,2), in which direction does f have the maximum rate of change? Note: The direction is specified by a vector

Q: Find sets of parametric equations and symmetric equations of the line that passes through the two…

A:

Q: 1. Calculate the derivative of y with respect to x. Express derivative in terms of x and y. e2xy =…

A: We are authorized to answer one question at a time, so we are answering the first one. Please repost…

Q: (x, y) = f(x)=x√x + 12 DNE Determine the open intervals on which the graph of the function is…

A: Given query is to find the interval where function is concave up.

Q: Where does the normal line to the ellipse x² - xy + y² = = 3 at the point (-1, 1) intersect the…

A:

Q: Let A = {2,7,8}, B = {-1,2,6,7}, C = {2,4,6,8,10}, D = {{7},{2,4},{6},2 ,8} List each set starting…

A:

Q: No sorry it wasn't meant to be done for each individual one, it's one option for the listed ones…

A: Given, the equation of a helix:rt=bcost i+ bsint j +1-b2 k We need to find the interval of t to find…

Q: Use the method of Lagrange multipliers to find the point/s on the parabola y = 3x2 that is/are…

A: Let's find closest point to (0,3).

Q: The linear approximation at x = 0 to f(x) = sin(4x) is: L(x) =

A: n

Q: of

A:

Q: A farmer is going to divide her 40 acre farm between two crops. Seed for crop A costs $20 per acre.…

A: NOTE: Refresh your page if you can't see any equations. . x=number of acres of crop A y=number of…

Q: Find the extreme values of g(x, y) = x² + y² + x²y on the circle x² + y² = 12 using the method of…

A: maximum value=28 minimum value=-4

Q: Use Implicit Differentiation to find f'(1/4) at (1/4 , 1/4) where y=f(x) and sin^2 (pix) +…

A:

Q: Let Find f (A) (B) el 2 (7) -2x sin x + cos x (C) 1 (D) (E) -√2 (F) 0 (G) 2 (H) None of these

A: Given query is find indicated derivative.

Q: Find the derivative of y with respect to t: y = sec¯¹ (9t5 + 8). dy dt

A: Given; y=sec-1(9t5+8).

Q: 17. Find the volume of the solid generated by revolving the region bounded by the graphs of the…

A:

Q: f(x) = √√x and g(x) = x² − 4x, find the following and their domains:

A: Given function:- fx=x and gx=x2-4x

Q: 1. Determine whether or not the following relations are functions. If the given relation is a…

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

Q: Let f (x) = √√x² +8. f'(x) = f'(2) = Number f"(x) = f" (2) = Number

A:

Q: 6. dx-2xcsc dy 11 2y - 2x³ cos 2y sec 2y a. b. C. d. e. f. g. h. i. j. C = ln 1 y² = ex s = [C(x -…

A: We know, 2sinx*cosx=sin2x csc2mx-cot2mx=1, for any real m ∫csc2mxdx=-cotmxm ∫cotxdx=ln|sinx|…

Q: If - xy + y = -4 then find point (2, 4) in simplest form. dy dx² at the

A: We need to find out the double derivative of the function at (2, 4).

Q: The region bounded by the given curves is rotated about the specified axis. Find the volume V of the…

A:

Q: Consider the points below. P(1, 0, 1),  Q(−2, 1, 3),  R(6, 2, 5) (a) Find a nonzero vector…

A:

Q: Limits 1. Below is a graph of the function g(x), find each limit as listed below. If the limit does…

A: As per the rules of the company we are supposed to answer the first question and rest can be…

Q: Find the arc length of the graph of the function over the indicated interval. 3 2 (x² + 1)² [0,1] 2…

A:

Q: Use implicit differentiation to find ∂z/∂x and ∂z/∂y. yz = 4 ln(x + z)

A:

Q: 2 8 I Identify the factors of each expression to figure out the name of the Indian mathematician who…

A: Here, We have given some algebraic expressions now we have to find out their factors and then we…

Q: lim Z-0 /52 +196 – 14 I

A:

Q: Suppose f is a one-to-one differentiable function and its inverse f^-1 is also differentiable.  a).…

A:

Q: 92. A cylindrical gasoline tank is placed so that the axis of the cylinder is horizontal. Find the…

A: It is given that, Diameter = 2 feetRadius = 1 ftρ=42 pounds/ft3

Q: (coth²(x))

A:

Q: The domain of f(x)= 2x+4 x²-x-2 a. is: All real numbers except -1 and 2 b. All real numbers greater…

A:

Q: 1. g(x)= 3tan 3x 2. y=x sin¹2x+cot¹ √x 3. f(x)=sin ¹. ¹ 4. y = (arc csc 2x) 5. G(x) = 5x Cos ¹2x 6.…

A: Let's find derivative.

Q: Solve the following differential equations. xy dx + (x2 - 3y) dy =0

A: Given, xy dx + (x2 - 3y) dy =0

Q: Sketch the graph of a function f having the given characteristics. (Select the correct graph.) f(0)…

A: Given query is to graph the function with indicated characteristics.

Q: Use the Chain Rule to find an equation of the tangent line to the curve of f(x)=tan(pix^2 /8) at the…

A: I am attaching image so that you understand each and every step.

Q: y varies jointly as x and z and inversely as w, and y=3/2 when x = 2,z = 3 and w = 4. Please explain…

A: Given,y varies jointly as x and z and inversely as w,  y=xzw

Q: If − xy² + x² − 4 = -y³ and it is known - y²-2x -2xy+3y² 9 points on the curve where y line tangent…

A:

Q: Gravel is being dumped from a conveyor belt at a rate of 50 cubic feet per minute. It forms a pile…

A:

Q: +6. Consider the function f(x) = 3x + Enter the number of critical points/numbers of f(x). 2…

A:

Q: verify that the function y = C₁ x ² + C₂ x ³ is a the differential equation: solution to and 2 x ²y"…

A:

Q: If √x + √√y = 12 and y(9) 81, find y' (9) by implicit differentiation. =

A: Given, x+y=12y(9)=81   Aim: Find y'(9)

Q: Weight of an Astronaut. The weight W on an object varies inversely as the square of the distanced d…

A:

Q: d²y If -y = 3x xy then find dy at the dx² point (2, 6) in simplest form. -

A: The function is given by -y = 3x-xy The point is x, y = 2, 6 To evaluate: The value of d2ydx2 at the…

Q: The rectangles in the graph below illustrate a left endpoint Riemann sum for f(x) = + 2x on the…

A: Concept: A basic calculus strategy is to start by providing an approximation for a given issue, then…

Q: and the radius and center of the sphere. [Hint: Complete the square in each va x² + y² +z² - 4x-8y =…

A:

Q: Find the exact length of the curve. y = 2x3/2, 0≤x≤6

A:

Q: For the function f(x) 4 v7-51 use the definition of the derivative to find /'(x).

A:

Q: Differentiate the function. R(q) = 7 lnq

A:

Q: The scalar projection of the vector onto the vector is: 6 10 3√5 10 7 1123 BC CC DC

A: See the details solution in below

Q: The height (feet) of a ball launched in the air t seconds after it is launched is given by: f(t) = -…

A: