Tlake Home part of lest 1. Find the critical values. for f(x) = x² + 4x³+4x²

Q: Find equations of level curves containing a point Find an equation of the level curve of the…

A: Given fx, y=y2arctanx

Q: 5. Let m be a constant. For x ≥ 0, the line y = ma divides the region enclosed between y = 2x - ²…

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Q: 19. a) Find an equation of the circle that satisfies the stated conditions. Center at the origin,…

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Q: 47-48 Simplifying a Difference Quotient Simplify using the 1101 Binomial Theorem. (x + h) ³ - x³ h…

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Q: If x² + y² + z² = 9, dz dt = dx Š dt dy dt = 4, and = 3, find dz dt when (x, y, z) = (2, 2, 1).

A: x2+y2+z2=9 dxdt=4 and dydt=3 (x,y,z)=(2,2,1)   Differentiate the given function with respect to t:…

Q: Write Equations of a Plane in Space Find the equation of a plane through the points (1, 2, — 7), ( –…

A: The objective of the question is determine the equation of the plane.

Q: Find the minimum of ƒ(x, y, z) = x² + y² + z² subject to the two constraints x + y + z = 1 and 2x +…

A: Given :- fx,y,z=x2+y2+z2Subject to constraints x+y+z=12x+3y+4z=8

Q: Given that u is a differentiable function, how do we get y' of y = arc csc(u)? T -^= f (x),n. (x),n.…

A: We can solve this as follows:

Q: Find the inverse transform of the given function of s. = 6s - 49 s²-85+41

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Q: In Exercises 13-16, find and sketch the level curves f(x, y) = c on the same set of coordinate axes…

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Q: i am just very confused, i know all of this is correct but i dont know the basic rules of sets

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Q: and x³ and y = √√√x. Find the area enclosed between the curves y = x³

A: We can find the area between the curves.

Q: - 2q + 250, where q is the quantity Let the demand function for a product be given by the function…

A: Given,Demand Function D(q) = -2q + 250(A) Revenue from selling 105 itemsRevenue function = q ×…

Q: Find the distance (d) between the planes x d = - 3y + 2z = 3 and x 3y + 2z = 1.

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Q: Obtain the differential equation of this family of curves. The lemniscate ² = acos 20

A: see below the answer and calculation

Q: The expression sec² x tan³ x √tan² x+16 Otrigonometric substitution O algebraic substitution O…

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Q: 4. Find the general solution to the DE 2x²y + xy'-3y=0.given that y₁=- is solution.

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Q: Sketch the region enclosed by the given curves. Decide whether to integrate with respect to x or y.…

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Q: Find an equation for the tangent plane to the surface 6 z + 2 = xy cos(z) at the point (2, 1, 0).…

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Q: ניע dv 32 dt 11 a) Write the given first-order LDE in standard form. b) Solve for the general…

A: Note - As per our guidelines we have to answer only the first three sub parts if multiple parts are…

Q: Sketch the region enclosed by the given curves. Decide whether to integrate with respect to x or y.…

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Q: Concept check: Evaluate the following integrals and use the appropriate transformations when needed.…

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Q: Find the inverse transform of the given function of s. 3 √ 55/2 F(s) = A B There is no correct…

A: We have to find the inverse transform of  Fs = 34πs52.

Q: The volume of a box is 10x3 + 27x2 + 2x - 24 with the length 5x - 4 and the width 2x + 3. Find the…

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Q: Which of the is the best transformation of f trigonometric substitution? Of sec 0 de Of 5 sec 0 de O…

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Q: Find y' if 7 y² + sin (3x) = 12-y f

A: Here we can find the y' in the below steps, using implicit differentiation.

Q: How long is the radius of the circle with center at (-4,5) and tangent to the y- axis?

A: Given query is to find the radius of the circle.

Q: Given: y = 5 (cosh log )², find y' (cosh² O g = =|sinh 2 log = ]5 sh®log }} O 5 O ý =−}(m& )[sinh 2…

A: The objective of the question is determine the derivative of the given function and choose the…

Q: How much do the volume of a sphere change with respect to its diameter at the instant, and the…

A: Recall: Volume of sphere, V=43πr3

Q: d csc 0 if tan 0 = 0 = and terminates in QII. Answer exactly. 15 Preview TIP Enter your answer as a…

A: Topic:- trigonometry ratios

Q: So So Va² +8 dx dy x=√y

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Q: (a) Find the dy = differential dy. y = ex/2

A: We will use differentiation to solve this.

Q: f(x) = z3 + 6 +6 3-4x-2

A: If y=u/v  then y'= (v×u'-u×v')/v2

Q: Find the distance from the point (-2, 8, 9) to the line ā(t) = ( − 1, 3, 2)t + (− 2, 3, 9).

A: To find the distance from the point -2, -8, 9 to the line a→t=-1, 3, 2t+-2, 3, 9.

Q: Find the vector equation that represents the curve of intersection of the paraboloid z = surface x =…

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Q: Differentiate each function with respect to x -- Product Rule. Please express in descending powers…

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Q: A certain isotope has a mass of 50 grams. It’s half life is 100 days. Write the equation that will…

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Q: Applications of Planes in Space Find the acute angle (in degrees) between the planes - 2x - 4y + 2z…

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Q: f(x) || = ex 1 - ex

A: ddxex1-ex

Q: 28. (2A + B²)4

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Q: 4. y" -10y +34y = -cos3x

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Q: Step 2 Now write the derivative in terms of x by recalling that u = x³ = x + 8. [eu] = (eu) du dx…

A: I have solved step by step in detail....go through the solution

Q: If a and h are real numbers, find the following values for the given function. The function is…

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Q: M3.2. d. A cadet engineer determines that when x hundreds of units of a particular commodity are…

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Q: 4 Let f(x)=x²-3x-2380, x>0.75. Find the value of df-1 At x = 0, dx (Type an exact answer in…

A: Given function:- fx=x4-3x-2380

Q: Problem 5. Consider the curves y = 4x, y = 1/x and y = 1. (a) (b) Graph all the curves to visualize…

A: Let's graph the given curves and find area of region.

Q: (c) d (100K+200) ((-1)u) p (p)

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Q: Question 3 An isotope of tin (Sn) has a half-life of 126 days. What is its decay constant? -5.5x10-3…

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Q: I need the P prime and Q prime of 1 and 6 P'(1)= Q'(1)= P'(6)= Q'(6)=

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Q: Find two positive numbers satisfying the given requirements. The product is 1200 and the sum of the…

A: Let the number be x and y Given: xy = 1200 To find x, y for which x + 3y is minimum