Find the absolute maximum and minimum vaules of the funct ion g(x)= (x^2-3x+4)/(x-1) on the interval [2,4].

Q: 2. As an application of partial derivative of multi-variable functions, provide one page abou…

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Q: Find the firct derivatioves of the follwing: - 3 ) y= 3x-x -2 4) y: Jerx 2) y: Ji-7x 5) y = 2メ-3

A: ddxxn=nxn-1 ddxu(x)v(x)=v(x)ddx(u(x))-u(x)ddx(v(x))v(x)2

Q: Find the 3rd derivative of the function y = (3x³ – 7x2 +5) (x²+5) O y" = 120z2 - 168z + 90 %3D O g"…

A: Recall:Firstly product the givern term and find function of 'x'   i.e;   y=fxSome formula:∙ddx…

Q: Find the critical points of f(x) and use the Second Derivative Test (if possible) to determine…

A: Given that the function is        f(x) = x e-x^2

Q: give 3 examples of the reciprocal rule of integration formula

A: The reciprocal rule for the integration is: ∫f'(x)f(x)dx=ln |f(x)|+C

Q: max value for y

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Q: Find the number x in the interval-;,1| so that the difference of the number from thrice'its cube is…

A: How to find point where the function f(x)  is minimum: find f'(x) and solve f'(x) = 0 for x. after…

Q: coat of paint of thickness 0.07 cm is to be applied uniformly to the faces of a cube of edge 40 cm.

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Q: Q-3-Edaluate the fallowing Integration 1- X3 x21 2. 2- X+1

A: Use the partial fraction to solve the given problem.

Q: 16. Sinusoidal functions do not have any critical points.

A: False. Sinusoidal functions has critical points.

Q: Use second derivative test, If f(x) = 25x + 10 then f(x) has a 3 local maximum at the point_

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Q: A basketball player makes a successful shot from the free throw line. Suppose that the path of the…

A: We have given that in the basketball game ,the ball travels the path given by y=2.15+2.09x-0.41x2…

Q: evaluate using the appropriate method or combination of methods.

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Q: Solve using variation OF patometert O reductian OF order CD-+)y= secx csc x csc X

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Q: By using the second derivative test for functions of two variables, find three positive numbers…

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Q: The normal line to the curve y = -2x2 at a point in the fourth quadrant passes through the point…

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Q: Find the critical points of the function by using algebraic partial derivatives test. Rx, у) - -х2 -…

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Q: Find the general solution. Orthogonal Trajectories

A: To Find :  General solution of Orthogonal trajectory of following

Q: Find  y ″  by implicit differentiation. 2x3 − 5y3 = 5

A: We will differentiate w.r.t x twice using the product rule and the chain rule

Q: he first derivative of y = 3x ++ 2V - a is %3D 3 10 y' 5 5z 5 3z 3 3 O y' 10 %3D 2V14 3 O y' 3. 10…

A: To find the derivative of: y=3x15-23x+35+2x34-5x23⇒y=3x15-23x+35+2x34-5x-23...(1) Note that:…

Q: ne side of a right triangle is known to be 150 cm long and the adjacent angle is measured as π/ 3…

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Q: An ant is standing at the point (1,1,3) on the surface of a bowl with equationz=x^2+…

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Q: Find two positive numbers with product 289 and whose sum is a minimum.   Enter your answers in…

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Q: The second derivative test fails when f" is zero or does not exist at the critical number of the…

A: Given data: The value of the second derivative of the function is f''=0.  Suppose at the given point…

Q: do you agree that cubic function must have at least 1 x - intercept but not more than 3 whereas…

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Q: aresin (2x-1) = 1-x 2 arctan

A: Substitute x = cos^2(theta) and simplify the equation.

Q: Fin derivative of the funclions. y=Log

A: The given function is: y=log3xx-12

Q: A metal storage tank with fixed volume V0 = 360π m^3 is to be constructed in the shape of a right…

A: To find: The dimensions will require the least amount of metal. Given information: A metal storage…

Q: find all possible functions with the givenderivative. y' = √θ - sec2 θ

A: Given: y'=dydθ=θ-sec2θ for evaluating solution of given differential equation, we use variable…

Q: The length and width of a rectangle are measured as 89 cm and 22 cm, respectively. The error in…

A: According to the given information:Length of rectangle (l) = 89cmWidth of rectangle (b) = 22cmError…

Q: ди ди x====u+Yay ?х

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Q: (b) Use the First Derivative Test to identify all local extrema. Local minimum at x = Local maxiтит…

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Q: Find the derivative of f (x ) =V sech( In (8x + 1)) - sech(In(8x + 1)) tanh( In(8x + 1)) A 2/ sech(…

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Q: Find 2. dy of 2.

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Q: Please show me the partial derivatives for this homogenous equation and solve for GS/PS using Test…

A: Exact differential equation

Q: Suppose that a drug is administered to a person in a single dose, and assume that the drug does not…

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Q: Integrate xtanx with respect to x

A: We have to solve this integral by  Integration by parts rule, Formula is  ∫uvdx=u∫vdx-∫u'∫vdxdx

Q: Determine the Derivative of the Function: 1. y = ex - 1/ex + 1 2. y = x22x 3. y = 43x^2 4. f(x)…

A: Find derivatives

Q: A basketball player makes a successful shot from the free throw line. Suppose that the path of the…

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Q: 6(2tanx - x^4 + 4lnx)^1/4(2sec^2x - 4x^3 +4/x)dx. Hint: let u = 2 tanx - x^4 + 4lnx

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Q: Explain how to find a first partial derivative of a function oftwo variables.

A: To get the first partial derivative of a function z = f(x, y) with respect to x we have to…

Q: Solve using partial differentiation

A: Given that  uxy=4eycos2x given that y = 0, ∂u∂y=cosx and u=y2…

Q: A flexible stretched string is constrained to move with zero slope at one end x=0, while the other…

A: Given: A flexible stretched string is constrained to move with zero slope at one end x=0, while the…

Q: Find 1" and 2nd order partial derivative for the function ax²+by²+2hxy and also verify дхду дудх

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Q: Find all critical numbers and use the Second Derivative Test to determine all local extrema.

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Q: When should I use partial integration and when should I use substitution?

A: When should I use partial integration and when should I use substitution.

Q: Find the orthogonal trajectories of the functen X + ce-X which is . passing Thieugh (-2.0)

A: We need to find the orthogonal trajectories of the function y=x+ce-x, which is passing through (-2,…