Verify that f has an inverse function. Then use the function f and the given real number a to find (f¹)'(a). f(x)=√x-9, x>9 a = 2

Q: Your are driving away from Tampa. Your distance (in miles) away from Tampa x hours after 12:00 noon…

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Q: III. Solve the following problems. 1. A manufacturer of tin boxes wishes to make open boxes from…

A: A manufacturer of tin boxes wishes to make open boxes from pieces of tin withdimensions 8 in. by 15…

Q: The height (feet) of an object launched in the air t seconds after launch is given by s= - 16t²…

A: see below the answer with explanation

Q: The total revenue (in hundreds of dollars) from the sale of x spas and y solar heaters is…

A: This is a problem related to maxima and minima of the function. Based on the general formula and…

Q: y = 1 x=y² B A (0,0) y=x² C (1, 1) X=1 X

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Q: 2. If Ac B then BCA.

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Q: a) Approximate the area under graph (a) of f(x) = 2/x² over the interval [2,6] by computing the area…

A: Area using rectangle

Q: For the function f(x,y)= x + 4y 3 4 x +y find f, fy, f(5,-5), and f,(1,3).

A: For the function fx, y=x2+4y3x3+y4, to find fx, fy, fx5, -5, and fy1, 3.

Q: Consider the following: (5/2,1), (-9/2, 8/3) Find the distance between these points.

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Q: Find the derivative of the function. g(x) = ((7x^2-4)/(4x+7)^-2

A: We have to find the derivative

Q: Differentiate Expressions

A: This question can be solved using the concept of differentiation of trigonometric functions.

Q: Let f(x,y) = 8x - 2y + 5. Find the following values of f(x,y) for the given coordinates. (a) f(2,…

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Q: Find the slope of the graph of the function at the given point. Use the derivative feature of a…

A: Solution

Q: Given the vecor-valued function R(t) = cosht i ln(t+1) j+et k, find lim h→0 R(0+ h) - R(0) h O…

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Q: 10. f(x, y) = x/(x² + y²)

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Q: 5. A function u(x, y) is defined by u2³-3xy². (a) Show that u is harmonic, i.e. it satisfies…

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Q: .. Find the derivative of each of the following functions:- 1. y=(sin ¹x²+ 1+tan x

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Q: dy dr = cos(²) +

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Q: Match the following functions with the appropriate cross-section: I) z = (y²-1) cos(x) II) z=(x²-1)…

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Q: Find the maximum profit and the number of units that must be produced and sold in order to yield the…

A: To find: Maximum profit

Q: Q14) [2x (1+x²) x-(1-x²) (1+x²) +CB)- 10 (1+x¹) (1+x²) (1+x²)" (1+x²)" 11 +00) +CD) 11 10 12 1.1…

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Q: (B) Use Tabular integration to evaluate the following: - f(t³-4t² + 5t+ 32) sin(t)dt

A: The tabular integration is a process of evaluating the integral using integration by parts. In this…

Q: Given cost and price (demand) functions C(q) = 110q+44,000 and p(q) = -1.8q +850, what is the…

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Q: differentiate 3thetacos(2theta)+2sin(2theta)

A: A detailed solution is given below.

Q: 1. (3x - 2y + 1) dx + (3x - 2y + 3) dy = 0.

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

Q: noon and 2 pm the population triples, at what time should the population become 100 times what it…

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Q: The function f(x) = = √x 2+√√4x is. increasing on its natural domain increasing on (2, 3) and…

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Q: to evaluate the following: f(t³-4t² + 5t+ 32) sin(t)dt (B) Use Tabular integration

A: Given integral is :

Q: Use the given information to find A. A-1 [$3 4 5 5 12 NOTE: Write the elements of the matrix…

A: Topic = Matrix

Q: problem: A rectangle has a perimeter of 120 meters. What dimensions yield a maximum area? Let the…

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Q: 4. If u = xy + y²z³, where x = rset, y = rs²e when r = 2, s = 1,t = 0.

A: We have to find solution

Q: Use Taylor's Theorem to find an interval [ z, z] where the Maclaurin polynomial p2(x) = 1- 2 1…

A: Given problem  is :

Q: Find the vertical asymptotes (if any) of the graph of the function. (Use n as an arbitrary integer…

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Q: A rectangle is to be inscribed in an isosceles right triangle in such a way that one vertex of the…

A: A rectangle is to be inscribed in an isosceles right triangle in such a way that one vertex of the…

Q: Set up the triple integral that will give the following: (b) the volume of the solid B that lies…

A: Let's find volume of solid.

Q: AY (1, 1) A X=1 y=x² с X (0,0) = 1, and the y-axis. Region A is bounded by the parabola x = y², the…

A: Note : As per our guidelines we are supposed to answer only 3  subparts if there are multiple…

Q: Solve the given by simple substitution (2x + y)² dx - 2dy = 0

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Q: (a) Use the Maclaurin series, In(1 + x) = x -+-+ = E=1(−1)n+12², 2 X to derive the series expansion…

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Q: y = 1 (1,1) A X=1 y=x² C X (0,0) Region A is bounded by the parabola x = y², the line y = 1, and the…

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Q: Consider Mean Value theorem for derivative for function f(x) 4(1-2x) in interval [0,1]. TCOS(TX) -

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Q: 9. Find a unit vector perpendicular to both [1,2,-3] and [2, -1, 4].

A: Given a=i+2j-3k b=2i-j+4k Aim : to find unit vector perpendicular to a and b

Q: 2. f(x) = √x²-4 if x<2; √x-2 if x≥2 ; a= 2

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Q: Show that the Fourier series of is: 2 ƒ (a) = (1/2 + 1). - Σ n=1,3,5,00 1 1 Hence find the sum of…

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Q: (a) Any critical point of a function f is either a local maximum or local minimum for f. True False…

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Q: 2. A basketball is being filled with air at a rate of 6 in /sec. (You can assume the basketball is a…

A: Given change in volme dV/dt= 6in3/sec Radius of ball is r= 1in then diameter   d= 2in Formula:…

Q: Find the root of f(x)=(x^2)-5, in interval [0,4] by using bisection method.

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Q: Evaluate the difference quotient f(a + h) - f(a) / h for the function f(x) = x ^ 2 + 4x - 5

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Q: Determine the antiderivatives of the following functions: 4. f(3x² +1)4 x dx 5. s dx

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Q: Find the absolute extrema of f on the given closed interval. 1. f(x)= x³ + 3x² - 9x ; [-4,4]

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Q: Let y=-4x. As x approaches negative infinite then y approaches -3 True or False

A: Consider the statement Let y=-4x. As x approaches negative infinite then y approaches -3