Find the critical point of the function f(x, y) = – (25x + 5y + In(|x + y[)). c = Use the Second Derivative Test to determine whether it is O A. a local minimum OB. a local maximum C. test fails O D. a saddle point (:) + (2)* - If C is the part of the circle = 1 in the first quadrant, find the following line integral with respect to arc length. (7х — Зу)ds %3D

Q: Tokal dexivetive of f i) Fxy)=In(xy), kind at xzl yal.

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Q: dy sin x - y where f(n) = 0. dx %D |

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Q: (a) By using thẻ chain rülé and the dérivative (1, (1xl) = {"1, if x>0 if x<0' d %3D dx 1-1, find -…

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Q: `s): The area of the surface obtained by rotating the curve y = ln(3x - 2), for 3 ≤ x ≤ e², about…

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Q: find a general sulution to the differential eguatiun using variation of A parametert b)yィyニ tantee…

A: Method of Variation of Parameters: This method is quite general and applies to equations of the form…

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A: Please check step 2 for solution

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Q: 1. Find the total derivative dz/dy, given (a) z = f(x, y) = 5x + xy - y2, where x = g(y) = 3y² (b)…

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Q: Find dw/ds and dw/at using the appropriate Chain Rule. Function Values w = sin(4x + 5y) X = s + t, y…

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Q: If m s f(x) < M for a sx s b, where m is the absolute minimum and M is the absolute maximum of f on…

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Q: Using u = 1 + t°, the limits of integration will change from t = 0 to u = and from t = 1 to u =

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Q: Find the equation of the tangent plane to g ( x , y ) = e x cos ⁡ ( y )  at ( 0 , π ). Does g have a…

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Q: -x), with respect to OY. 4. The area bounded by the curve 2x+2x -y -2 0 and the line y=2x with…

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Q: In a mass-spring-dashpot system , the mass’s position at time t isy = 4e-t(sin t - cos t), t ≥…

A: Given: y=4e-tsint-cost, t≥0 The average value of y over the interval 0≤t≤2π

Q: Consider the curve segments: 1 S1: y = x from x =to x = 4 and %3D 2 1 S2: y = Vi from x = - to x =…

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Q: Given the function f(x,y) cos 2xーx3eY +āyン COS find te second partial olerivative fxy.

A: Let f(x,y) is the given function.Then  fx is the derivative of f with respect to x taking y as a…

Q: Consider the curve segments: 1 S1: y = x from x = to x = 3 and %3D 3 1 S2: y = Va from x =to x = 9.…

A: To find the arc length of the given two curves.

Q: Which of the following definite integrals gives the length of the arc y - 1 + 16x-dy 0 16y – 15 이 0…

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Q: Consider the curve segments: S1: y = x from x = 1 to x = 2 and 1 S2: y = Vx from x =to x = 4. Set up…

A: Let's find.

Q: Assuming that f(x, y) is an integrable function, which of the two cross-sections would you choose to…

A: As per the question we are given a 2d region of integration defined as the area bounded by : y = ex…

Q: Find a solution for the DE subject to the indicated initial condition: dy dx + P(x)y= x, y(0) = 1,…

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Q: · Use fourth-order Runge-Kutta Method to solve the following problem over the interval from x 0 to…

A: The given differential equation is,  dydx=y'=-3y+2e-x with an initial condition y0=2.  For…

Q: 4. Supposea function y = f(x) is so be revokved at x = e from point (a, b) to (c, d), what is the…

A: Please refer the attached image for complete solution.

Q: dy (a) Obtain the integral curve for dx y-x passing through the point (1, 0). y+x (b) Find the…

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Q: A particle moves on the circle x2+y2=25 in the xy-plane for time t≥0. At the time when the particle…

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Q: 1, use 2x2 + 3x + 2. If Ax linear approximation to estimate Ay Let y 0.4 at x = Ay 2

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Q: 1. Find the total derivative dz/dy, given (a) z= f(x, y) = 5x + xy – y², where x = 9(y) = 3 y2 (b)…

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Q: Find the path y = y(x) for which the integral 1. r2 VaVi+y(xdx is stationary.

A: The path y = y(x) for which the integral is stationary satisfies Euler’s equation given by,

Q: of Let f (x,y)=tanh-1(x-y) with x=e" and y= usinh (t). Then the value of evaluated at the point dt…

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Q: Consider the curve segments: 1 S1: y = x from x = to x = 3 and S2: y = Vx from x = 1 -to x = 9. 16…

A: Use formula of length of arc

Q: Set up the integral used to find the length of the curve y = V1-25 on the interval -<zs Select the…

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Q: Determine the total differential (dg), and total derivative with respect to x 3x 2y f(x, y, z) =…

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Q: Use fourth-order Runge-Kutta Method to solve the following problem over the interval from x = 0 to…

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Q: If m s f(x) s M for a sxsb, where m is the absolute minimum and M is the absolute maximum of f on…

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Q: Find the length L of the arc formed by y = (-4x² + 2 In(x)) from x = 4 to x = 5 8 Set up: L = V1+…

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Q: Evaluate the deflection of a vibrating string of unit length having fixed ends with initial velocity…

A: Consider the wave equation    ∂^2u∂x2=1c2∂^2u∂t2     .....(1)   here U(x ,t) is the defection of the…

Q: Evaluate the integral - T/2 (8 + 4cosx)dx 0. Using:

A: The given integral is ∫0π28+4cosxdx In part (a), we shall solve it analytically, and in part (b), we…

Q: 1- f(x, y) dy dx •x+1 f(x, y) dy dx + at is the sum of the four resulting limits of integration? 3.

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Q: find the general selution of the differential equetion by the fimear methodi sxy'-2y=x

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Q: If m s f(x) s M for a sxs b, where m is the absolute minimum and M is the absolute maximum of f on…

A: Solution ) smaller value   = m (b - a ) b = 4π , a = 3π m = ( 8x - 16 sinx ) at x = 3π m = ( 8 × 3π…

Q: 2.a) Apply the Trapezoid and corrected trapezoid rule, with h = 1, to approximate the integral 1 dx…

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Q: Consider the curve segments: 1 S1: y = x from x =to x = 4 and 3 1 S2: y = Väfrom x =- to x = 16. Set…

A: We have to set up the integral that give the arc lengths of the curve segments. S1: y=x2 from x=13…

Q: The integral that represents the arc-length of the curve y = In x, xE [2,3] is: %3D 3 x2+1 dx. Vx2+1…

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Q: Find dw/ds and dw/at using the appropriate Chain Rule. Function Values w = sin(4x + 5y) x = s + t, y…

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Q: (c) Determine the arbitrary constant of integration for the integral: y = [(4t -5-dt given that y =…

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Q: 4. Given f(x, y) = arctan(x + 2y). Find the local linear approximation of f at (1,0) and use it to…

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Q: Suppose a function y = f(x) is so be revolved at x = e from point (a,b) to (c, d), what is the…

A: The surface area generated by revolving the curve y = f(x) between x = a and x= b  revolved about x-…

Q: Consider the curve segments: S1: y = x* trom x = to x: 2 and S2: y = Vafrom x = to x = 4. 16 Set up…

A: Let S1:y=x2 from x=14 to x = 2 and  S2: y=x from x=116tox=4

Q: Consider the curve segments: S1: y = x from x =- to x = 2 and S2: y = 1 Vxfrom x = to x = 4. Set up…

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

Unitary Method

The word “unitary” comes from the word “unit”, which means a single and complete entity. In this method, we find the value of a unit product from the given number of products, and then we solve for the other number of products. 

Speed, Time, and Distance

Imagine you and 3 of your friends are planning to go to the playground at 6 in the evening. Your house is one mile away from the playground and one of your friends named Jim must start at 5 pm to reach the playground by walk. The other two friends are 3 miles away.

Profit and Loss

The amount earned or lost on the sale of one or more items is referred to as the profit or loss on that item.

Units and Measurements

Measurements and comparisons are the foundation of science and engineering. We, therefore, need rules that tell us how things are measured and compared. For these measurements and comparisons, we perform certain experiments, and we will need the experiments to set up the devices.