Evaluate the limit: x² lim 7-0 sin² (6x)

Q: Find fo g, go f, and go g. f(x) = x², g(x) = x − 1 (a) fog (b) gof (c) gog

A: The objective of this question is to find the composite functions f(g(x)), g(f(x)), and g(g(x))…

Q: A particle moves in the yz-plane along the curve represented by the vector-valued function r(t) = 2…

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Q: Use the graph of g in the figure to find the following values or state that they do not exist. a.…

A: By using the graph of  in the figure to find the following values or to state that they do no…

Q: z-6 Consider the function f(x) = 7+6) Of(x) has an oblique asymptote f(x) has a vertical asymptote…

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Q: Suppose that {n} is a sequence of real numbers satisfying lim xn = 1. Use n→∞ in the text book to…

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Q: Find the volume of the solid generated by revolving the region bounded by y=4√√x and the lines…

A: To find the volume of the solid generated by revolving the region bounded by  and the lines  about…

Q: Find the velocity, acceleration, and speed of a particle with position function r(t) = (-3t sint,…

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Q: Question content area top Part 1 Find the derivative of the function.   yequals=StartFraction ln x…

A: The objective of the question is to find the derivative of the function y = ln(x) / x^6. This is a…

Q: Find the volume of the area bound by y=x^3, y=0 and x=1 if rotated about x=2.  Use washer method.

A: Region is bounded by y=x3,y=0,x=1Rotating the region about x=2x=y1/30≤y≤1Using the washer method

Q: o hand written explanations. I need a step-by-step breakdown with solving C. At a price of…

A: The graph of a linear equation is a line. A linear equation has the form  where c is a constant and…

Q: DC Find the values of x for which the series Σ9(x-3)" converges. >2=0

A: S=∑n=0∞9(x−3)n

Q: The volume of the solid obtained by rotating the region enclosed by y = x², y = 4x, about the line =…

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Q: Use a definite integral to find the area of the region, and check your answer using an appropriate…

A: To determine the area under curvef(x)=x+7

Q: A conical tank with radius of 5 meters and height 15 meters is filled with water. Let a measure the…

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Q: On Exploration 4.3.3, what is a vertical asymptote for Question 1? Ox=0 x = π/8 x = 2n/3 Ox= π/2 x=л…

A: The objective of the question is to identify the vertical asymptote for a given function in…

Q: 15) Given the points: P(-1,5), 9 (3,4), a) Find the distance between Pand Q using distance (carb),…

A: We need to find distacne and length.

Q: -6 (a) lim_ f(x)= -1117 Consider the graph of y = f(x) above. State the values of each of the…

A: Given: To Find: To evaluate the following.Note: Since, the student has posted a question with…

Q: Find an equation for the graph sketched below -5 -4 -3 -2 -1 f(x) = 8 %7 6 + 5 4 3 2 P OA -7+ -8+

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Q: Revenue The revenue (in dollars) from the sale of a infant car seats is given by R(x) = 70x -0.02x²,…

A: The objective of the question is to find the derivative of the revenue function R(x) = 70x - 0.02x².…

Q: Evaluate each of the following expressions. Note: Enter 'DNE' if the limit does not exist or is not…

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Q: When using trigonometric substitution to solve an integral containing 4x2-9, which of the following…

A: To find the trigonometric substitution to solve an integral containing

Q: Solve the initial value problem for r as a vector function of t. dr 9 1/2, 1 t+1 = 2 k dt (t+1) i…

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Q: If r(t) = cos(-5t)i computer' (t) = + sin(−5t)j + Ok i+i+ k k+C and fr(t) dt = with C a constant…

A: we are given a vector function and we need to compute its derivative and integration.

Q: A contour map for a function f is shown. S

A: To estimate function value of f (3,6)

Q: Determine the equation of the vertical asymptote of the function below.

A: Given graph of function

Q: The partial fraction decomposition of x² f(x) = " and g(x) 48 = can be written in the form of f(x) X…

A: To find the partial fraction decomposition of .

Q: At what times in the interval 0<t<pi are the velocity vector and the acceleration vector of…

A: The objective of this question is to find the times in the interval 0 < t < pi when the…

Q: Find the area of the sector of a circle with radius 19 inches formed by a central angle of 290°:

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Q: How could I use integration by parts to find the integral of -infinity to 0 -te^-(s+a)t dt ? I am…

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Q: If h(x) = √√4 + 3fƒ(x), where ƒ(1) = 7 and ƒ'(1) = 4, find h'(1).

A: Given function

Q: f(x)=√√x+7-2, [0,5], f(c) = 1

A: To verify the Intermediate Value Theorem (IVT) for the given function  over the interval [0,5] with…

Q: Find the surface area of revolution about the x-axis of R. Surface area = f(x) = 2√x [**(a) dar…

A: Let  be the curve .To find the surface area of revolution about the x-axis of R.

Q: Find the volume of the given solid. 64 9 under the surface z = 7xy and above the triangle with…

A: The objective of this question is to find the volume of the solid that is under the surface z = 7xy…

Q: If a colony of bacteria starts with 1 bacterium and doubles in number every 20 minutes, how many…

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Q: If an object's position over time is given by the function d(t) = (t² + 3)e for t > 0, on what…

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Q: Given a function and x values for f ‘(x) = 0. Help use the Second Derivative Test to determine…

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Q: 0 = $₁ ² (f) A function f(x) such that H(x) = f(t)dt has a local maximum at x = 5. Give an example…

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Q: Volume Discount Jester Apparel sells custom promotional shirts. The table below shows the volume…

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Q: Find the linear approximation of the function f(x, y, z) = your answer to five decimal places.)…

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Q: (A) (B) Let f(x) = −5 – x². Find each of the following: - ƒ(5) – ƒ(2) 5-2 = f(2+ h) - f(2) h -7 =

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Q: Find the absolute maximum and minimum values of f on the set D. f(x, y) = x² + y² + x²y + 8, {(x, y)…

A: The given function is

Q: A particle moves along the x-axis so that its position at time 0 < t < 18 is given by x(t), whose…

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Q: Let g be a function such that g'(x) = (x-1)-². 3 Sºg' g'(x) dx converges or diverges. Show the work…

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Q: 1) show that the equation x² - 4x + y² +12y=9² representS a circle, and find its center (a, b) and…

A: The given equation .The objective is (a) to show that the equation represents a circle and find its…

Q: Find the absolute maximum f(x, y) = xy² + 3, absolute maximum value absolute minimum value and…

A: The objective of this question is to find the absolute maximum and minimum values of the function…

Q: Evaluate the limit Enter I for ∞, -l for -∞, and DNE if the limit does not exist. Limit= 1 6 1m (2²3…

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Q: The nationwide attendance per day for a certain motion picture can be approximated using the…

A: The objective of this question is to find the rate of change of the daily attendance for a motion…

Q: Given that lim f(x) = 0 x→a (a) lim lim g(x) = 0 x→a lim_h(x) = 1 x→a lim p(x) = ∞o x→a lim g(x) =…

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Q: Find the area under the line y = 2x between x = 1 and x = 3

A: we need to find out the area of the bounded region.'As per the company policy, we are supposed to…

Q: Obtain the general solution to the equation. dy y dx X ==+x+2 The general solution is y(x) = x + 2x…

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