Consider the following. f(x) = x² + 16 Find the critical numbers. (Enter your answers as a comma-separated list. If an answer does not exist, enter DNE.) X = Find the open intervals on which the function is increasing or decreasing. Use a graphing utility to verify your results. (Enter your answers using interval notation. If an answer does not exist, enter DNE.) increasing decreasing

Q: ketch the region of integration, reverse the order of integration, and evaluate the integral. 10 10…

A: First sketch the curve by use of the limit of integration.

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Q: 2. Use Calculus to find all local extrema of the function g(x)=x√3-x.

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Q: 11. Identify the horizontal asymptote of * 3 f(x) = +2 x-2 Oy=1 Oy=2 y=3 Oy=-2 Identify the domain…

A: Horizontal asymptote:If  then the line y=L is the horizontal asymptote of the function f(x)

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A: To find the equation of a line parallel to y=−4x+4 and passing through the point (4, -21), you can…

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Q: 1. Using the fundamental theorem of calculus part 1, along with properties of the definite integral…

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A: Given the table below gives the velocity of a runner at half-second intervals during the first three…

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Q: A formula for the derivative of a function f is given. How many critical numbers does f have? f'(x)…

A: The critical number refers to the value at which the first derivative f' (x) of the real valued…

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Q: Let f(v) = V v+17 v + 12 Determine the critical values of f. Write exact answers. Do not round off.…

A: A point x=c is  a critical point of the function f(x) if f(c) exists and if  f'(c) =0 or f'(c)…

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A: Note:-Since you asked multiple sub parts questions, according to our policy we can solve only first…

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…

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Q: Given: f(x)=4x-10 and g(x)=√x-6 Determine the following: (f-g)(10)=0 (HM)={ (fog)(7)=O -O (gf)(6) =…

A: The given functions are  and

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A: The given differential equation is

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Q: Suppose the solid W in the figure is one- quarter of a circular cylinder of height 4 and radius 6…

A: Suppose the solid W in the figure is a one quarter of a circular cylinder with a height 4 and radius…

Q: Find the area of the shaded region. -1.0 -0.5 y 8 6 y=3e 4 2 0.5 (1, 3e) y=3xet² 1.0 1.5 2.0 X +

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Q: Evaluate the following integral using trigonometric substitution. x² √√64-x² S dx

A: I=∫x264−x2dx

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Q: Find the absolute extrema (max and min) of f(x,y)=3x^2-2y^2 over the disc x^2+y^2<=1. Indicate all…

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Q: (a) Find parametric equations for the line segment that joins the point P(-1,-4, -3) to the point…

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Q: ii) Read the graph below and say whether limx→-3 f(x) exists: y=h(x) -9-8-7-6-5-4-3-2 9876 8+ 7+…

A: This is question of calculusHere graph is given We have to find limit of function.Further…

Q: f(x)=x²8x² + 5

A: f(x)=x4−8x2+5

Q: Evaluate the following integral, f (x - 5y) dx - 8y² dy where C' is given by x = y² + 6 from (7, 1)…

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Q: (a) Find and sketch the domain of the function f(x,y)=√x-1+√y-4

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Q: What is the minimum degree of the polynomial function whose graph approximates each given graph?…

A: Consider the graph

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Q: Express each function as a composition of two functions. (Find f(x) and g(x) such that the given…

A: We have to find the given function as a composition of two functions f and g.

Q: Find the differential of the function. dy = y = √ 8-t6

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Q: Find the volume of the region between the cylinder z = 2y² and the xy-plane that is bounded by the…

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Q: Put the following function in the form P(t) = Poekt. P(t) = 110(0.72) NOTE: Round your answer to…

A: If we need it in the form P = P0 ektGiven, the P0 term is there (it is 110)The only thing we need to…