Find z¸and zyif z = x² tan¯¹ (²) — y² tan¯ an-¹) y

Q: 1. In each of the following initial value problems, determine the maximal interval in which the…

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Q: (d) s

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Q: Show that xzxx+yzxy = y²Zyy if z = xy + yln(xy)

A: To prove the given result find zxx,zyy,zxy and substitute in the given equation.

Q: 3 Calculator active. Line L is tangent to the graph of y = 2 sin x at the point (k, 2 sin k), where…

A: Equation of tangent line L of a curve y=f(x)  at a point (a,b) is given byy-f(b)=f'(a)(x-a)

Q: Use the tabular method and the properties of limit to find the limit lim ex-4 X→4

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Q: Now using L'Hospital rule evaluate the following: sin x tan x a) lim x →0 x³ b) Evaluate the limit…

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Q: Find the volume of the parallelepiped with adjacent edges PQ, PR, and PS. P(-2, 1, 0), Q(4, 2, 4),…

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Q: Name: 1. Find the value of b for which the given equation is exact. Then solve it using that value…

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Q: Evaluate the limit: lim x-6 x² + x - 30 x + 6

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Q: Problem 1. For every real number a, compute the derivative of y = x4 at x = a as a limit of a…

A: As per our guidelines we are supposed to answer only one question. Kindly repost others question as…

Q: hello please help in assisting me with how to get the functions for this shape

A: NOTE: Refresh your page if you can't see any equations. .

Q: Match the equation with its graph. x² + 2z² = 1 X* x.

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Q: Let u, ER" prove that ||ū + ï|| ≤ ||ū|| + ||v||

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Q: Solve for the complete solution of the differential equation: 1. What is y(3)? y"+y' 2y = 0; y(0) =…

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Q: Solve the given initial value problems. y'' - 4y' + 4y = 0, y(1) = 1, y'(1) = 1

A: To find out the solution of the differential equation.

Q: Differentiate. y' = y = In (6x² − 5x + 1)

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Q: Use the graph of the function to find its domain and range. Write the domain and range in interval…

A: We have to find domain and range of a function from it's given graph.

Q: Find dy dx 14.) y = x¹ - 7x

A: To find derivative

Q: 2x Find the second derivative of y = e²x sin(3x)

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Q: 4. Determine the domain ONLY of f(x) = 4-x x²_9

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Q: Drum Tight Containers is designing an open-top, square-based, rectangular box that will have a…

A: we need to find out thr dimensions that will minimize the surface area

Q: Sketch the graph of a function f for which f(0) = 0, f'(0) = 3 , f'(1) = 0 , and f'(2) = -1.

A: Let equation of the function be, f(x)=ax³+bx²+cx+d ...(i), a,b,c,d are constants.

Q: Use the definition of derivative to find f'(x) and f"(x) f(x) = 4x² + 3x + 2 f'(x) =

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Q: Minimize the function M=3x² + 3y² subject to 2x+y=64 and find the values of x and y at which M is…

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Q: Find the difference quotient (z+h)-f(z) for the function given below. f(x) 1²+1+2 Give a simplified…

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Q: A mold grows at a rate that is proportional to the amount present. Initially there is 5 oz of this…

A: A mold grows at a rate that is proportional to the amount present. Initially there is 5 oz of this…

Q: Find the solution of the IVP: (1 + y cos x) dx - sin x dy = 0, y(1/2) = 1. Then, evaluate y(1.603).

A: This question can be solved using the concept of linear differential equation.

Q: Find the G.S. (6x+y2) dx + (2xy-3y2) dy =o

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Q: Find inverse g(x)=x²-2x, x²1 f(x)= 1+√2+3x S y = (2+ 3√x) ³ 1-√X Y = T+√x

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Q: 4. A boat is pushed off from a beach at 2m/sec. A man on shore holds a rope, tied to the boat, at a…

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Q: If f(x)  = 3x2 -x3, find f'(1) and use it to find an equation of the tangent line to the curve  y=…

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Q: Evaluate the integral. (If the quantity diverges, enter DIVERGES.) 9 0 dx 9 − x please…

A: Given, ∫09(9-x)dx

Q: (a) Show that y = e(c₁ cos x + c₂ sin ) is a general solution of y" + 2y' + 2y = 0. (b) Deter- mine…

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Q: Consider the graph below of the function g(x) to evaluate the integrals. The graph consists of two…

A: The integral is consist of area under two straight line and one semi circle

Q: Write cos(sin(x)) in an algebraic expression form.

A: the solution consists of substitution

Q: 2. A curve is defined by f(x) = a√√x+b, where a and b are constants. the point (4, 6), determine the…

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Q: 4. A large container initially contains 50 gallons of salt-water with concentration 0.4 lbs. of salt…

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Q: Given f(x, y, z) = xyz, find fyyx

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Q: A. A. Find if x = 2t4 - 4t² and y = t4 - 4t. dx t²-t+1 2t(t+1) B. t² +t+1 2t(t+1) Find f'(t) if f(t)…

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Q: z = x² + x - 3xy + y3 - 5, find all points (x, y) wherein zand zy = 0.

A: The points are (1/4,1/2) and (1,1) the detailed solution is given below

Q: Suppose that a certain car has the following average operating and ownership costs. Average Costs…

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Q: (a) Show that y = e(c₁ cosa + c₂ sin x) is a general solution of y" + 2y' + 2y = 0. (b) Deter- mine…

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Q: Use properties of limits and algebraic methods to find the limit, if it exists. (If the limit is…

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Q: Write a in the form a=a+T+aNN at the given value of t without finding T and N. r(t) @ = (?)i + (x +…

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Q: Find a formula for a function g(x,y,z)  whose level surfaces are planes parallel to the plane…

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Q: f(x) || { -४४० -122 X ++ x + 2 C if x # -2 (and x = 0) if x = -2

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Q: 2. f(x) = (x + 2)²³ (x-1)

A: Given:       fx=x+22x-1  Apply chain rule:   f·g'=f'·g+f·g' here f=x+22, g=x-1…

Q: Suppose the density of a wire is given by p(z) = 0.6 +0.09 sin(27) kg/m, where is the distance from…

A: NOTE: Refresh your page if you can't see any equations. . the given density function is the length…

Q: 51-52 Find an equation of the tangent line to the curve at the given point. 51. y = e* cos x + sin…

A: As per the company guidelines We can first question only. Please understand. Kindly repost the…

Q: Evaluate the integral. 6 t² sin(2t) dt

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