4. Use Calculus to graph g(x)=x² + 4x³. Make sure that your graph shows all intercepts, extrema, and inflection points. Show additional work on the back of the first page, if needed.

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A: An employee's monthly productivity M, in number of units produced, is found to be  a function of…

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A: y'(0)=1

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Q: Let 16x-5 1x² +5 Enter the exact value of the one-sided limit lim f(x) 3-2 f(x) = if x ≤ 2 if x > 2

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A: Radius = 60cmdr/dt = 0.01 cm/min.

Q: If z² = x² + y² with z > 0, dx/dt = 2, and dy/dt = 6, find dz/dt when x = 6 and y = 8. dz dt Answer:…

A: The Power Rule:The Chain Rule:

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Q: Find the differ y = √3 dy= = Evaluate dy fc x = 1, G y =

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Q: 8 3 dx √√x-3

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Q: Find the total differential. 8x + y 3z - 2y dw = W X

A: If W = f(x,y,z) then the total differential of W is given by   +

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A: In this question we will find the lowest and left most point.

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A: Given that Let

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Q: 2. Consider 1, 0.1, 0.01, 0.001, 0.0001, ... (a) Write out the next three terms of this sequence.…

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Q: 6. Given f(x) = 3x - 1 A. Find (f-g)(x) B. Find (fog)(x) report domain and simplify C. Find (3) (2)…

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Q: Evaluate the indefinite integral. Answer = +C St tan¹ (2x) dx

A: Let,  A=.

Q: Consider g(z) = -10z + 15z² - 9 Determine the intervals on which g is concave down. g is concave…

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Q: (3) Find the general solution of the following different equation (2x³ − xy² −2y + 3)dx − (x²y + 25…

A: Given Differential equation

Q: Evaluate the following integral using integration by parts. √x20 In x dx

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Q: Find the arc length of the curve on the given interval. Parametric Equations x= 7t + 5, y = 7 - 8t…

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Q: Find a formula for the nth partial sum of the telescoping series below and use it to determine if…

A: ∑n=1∞(n+6−n+5)

Q: (a) In(2x + 1) + In(10) = In(50) (b) (c) log(9x + 1) = 2 e2x - 3ex + 2 = 0

A: Given equations to solve for 'x'

Q: xª−12x³+36x² X-6 x4+x³-42x 2) lim ||

A: since you have posted multiple questions in this question which are not interlinked so i have solved…

Q: Use spherical coordinates. Evaluate xex + y2 t2 + dV, where E is the portion of the unit ball x² +…

A: To find  E is the portion of the unit ball  that lies in the first octant

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Q: Find the measures of the sides and angles. Round angle measures to the nearest tenth of a degree.…

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Q: Find the exact length of the curve. x = 7 cos(t) = cos(7t), y = 7 sin(t) sin(7t), - 0 ≤t≤n

A: x=7cos⁡(t)−cos⁡(7t),y=7sin⁡(t)−sin⁡(7t),0≤t≤π

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A: The Root Law:The Sum Law:

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A: SolutionLet f(x)=√x and use the linearization at a=100

Q: Solve | | - 3x +8 24

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Q: 1. Use Calculus to find the absolute extrema of f(x)=3x4-4x³ -36x² +28 on the interval [-3,4].

A: By using Calculus to find the absolute extrema of  on the interval .Note: Since the student has…

Q: y-values 9 8- 7 6 5- * 3 2 1 If f(x) f'(3) = g(x) 1 g(x) h(x) > 2 3 x-values then 4 y-values 4 3 2 1…

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Q: Use the remainder theorem to determine if the given number c is a zero of the polynomial. f(x) = 5x²…

A: Remainder Theorem:If a polynomial p(x) is divided by the binomial x−a,the remainder obtained is…