9) A rectangle has one corner on the graph of the line y = -x² + 6, another at the origin, a third on the positive y-axis, and a fourth on the positive x-axis. (See graph on the right.) (a) Express the area A of the rectangle as a function of x. (b) Express the perimeter of the rectangle as a function of x.

Q: Find the discontinuities of the function f(x) = = discontinuity and redefine if removable. x-1 ex x…

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Q: Use the theorem given below to find the curvature of r(t) = tj + tk. k(t) = Theorem: The curvature…

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Q: Use the tabular method and the properties of limit to find the limit lim x-1 2x + 2x 3

A: Given, limx→12x+2-x3

Q: • The domain off is (-∞, +∞0) •f (5)=-2 • x intercepts are -7, -5, -3, 0, and 3 • limf(x) = 0 x+5 •…

A: To Find: Create a function that satisfies all the conditions.

Q: Use the graph of y = f(x) to graph the function g(x)=f(x)-2 y = f(x) Q AY -6 -4 -2 -2 + ib N Choose…

A: Concept: A relation between a collection of inputs and outputs is known as a function. A function…

Q: (x + y − 5)dx + (3x + 3y + 2)dy = 0 -

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Q: Find the general solution of each of the following. J.. 1 1. in 2. y tan² x dx + In¹y dy = 0 000² v…

A: Please see the below picture for detailed solution.

Q: ONLY parts L, M, and N please show all work

A: Given Figure:

Q: From the information given, find the quadrant in which the terminal point determined by tt lies.…

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Q: f(x,y)=(5x°-4y3, + 4xy²

A:

Q: Consider the function below. f(x, y) = In(x + y - 3) (a) Evaluate f(1, 3). (b) Evaluate f(e, 3) (c)…

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Q: find the gradient of z = x² + y² - 3x4 at point (2, 1)

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Q: 1 23. Σ (Inn)" 0=1

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Q: Use the IVT (intermediate value theorem) to show that the given polynomial f(v)= 2v2 + 3 - 3v has a…

A: Here we have to use the intermediate value theorem.

Q: Use the tabular method and the properties of limit to find the limit 1) lim 2 X-0 х (²)

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Q: 20. 8] n=1 2² 5n+10

A: D'Alembert Test: Let ∑n=1∞un be a series such that, limn→∞un+1un<1 Then this series is…

Q: (e) Finally, consider f along rays emanating from the origin. Note that these are given by y = mx,…

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Q: 5 7 s(%)+{db)+ 6- 63-р +)+6=65 = p P 5

A: Given a differential equation.

Q: Q2: Use the substitution x² = sing to show that 1 √ √ ² x dx = [] 4√2TE

A: See this solution in below.

Q: the function y = x(x 6)².

A: To find the critical points for the given function

Q: Find the general solution of each of the following. rdp-(p+√pr)dr=0

A: Our Aim is to find the general solution of the following given below:-rdp-p+prdr=0 -(i)

Q: (1.1) Calculate the Laplace transform of the following function from first principles: f(t) = = 3t -…

A: Laplace transform of a function f(t)  using first principles is Fs=Lft=∫0∞e-stf(t)dt

Q: A company that sells calculators has determined that the revenue generated by selling x calculators…

A: Given, A company that sells calculators has determined that the revenue generated by selling x…

Q: Which of these is true? Explain briefly. a. 316 b. 36=2 C. 613

A:

Q: A. Exact Differential Equations Verify that the following DEs are exact, then find the general…

A: We can solve the given differential equation .

Q: The _____ of a long-linear plot is on a log scale A. X-axis B. Y-axis C. Both axes

A: Given question:- The _____ of a long-linear plot is on a log scale   A. X-axis   B. Y-axis   C. Both…

Q: A chemical reaction converts a certain chemical into another chemical, and the rate at which the…

A:

Q: Find f'(a). f'(a) = f(t) = 8t + 44 t + 7

A: Given query is to find the derivative of the expression.

Q: Find (f 1)' (a) f(x)=3x³+4x²+6×+5₁ a=5 f(x) = x³ +3 sinx + 2 cosx, q=2 f(x) = 3+x² + ton (₂),…

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Q: Find differential equations for the following families of curves: (a) x2 + cy² = 1, (b) y² = ax + b.

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Q: angle between 0∘0∘ and 360∘360∘ that is coterminal with the 1950∘1950∘ angle is what degrees.

A: Topic:- trigonometry

Q: 3-7 Use the method of cylindrical shells to find the volume generated by rotating the region bounded…

A: 7) Given:         y=x2 , y=6x-2x2 Equating the curves:     x2=6x-2x2     x2+2x2=6x     3x2=6x…

Q: If= 1π sin(0) = use the unit circle to find

A: Please refer to the image below

Q: 12.) Using the result from Problem 11, find the equation of the tangent line at (-2, -1/2).

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Q: (d) s

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Q: 1) Let f(x) Choose the best answer. = sin² (3x4). Derive the derivative f'(x).

A: The explanation of answer as follows

Q: 1. Pirkko wants to invest 9 000 euros so that after 8 years she will have 14 000 euros. What is the…

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Q: 10. Solve uxx + Uxt-20utt = 0, u(x, 0) = (x), u₁(x, 0) = (x).

A: Factor the operator as we did for the wave equation

Q: (cos X-cosy-cotx) dx - sinxsiny dy=0

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Q: -23+-13

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Q: n a circle of radius 6 miles, the length of the arc that subtends a central angle of 1 radians is…

A: Given:- Radius of circle r=6 miles Central angle =1 radians

Q: Integrate cos x dx with limits from 0 to π/2. A. 1/2 B. 3/2 C. 1 D. 2

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Q: 6 2²{ - 2s-8) 01 02 03 C 4+2 ett

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Q: Use the graph of y=f(x) shown to the right to graph the following function g g(x) = -f Choose the…

A: see below the answer and explanation

Q: Suppose that f is continuous on [0, 6] and that the only solutions of the equation f(x) = 3 are x =…

A: f is continuous on [0,6] and that the only solution of the equation f(x)=3 are x=1 and x=5.If f(4)=5…

Q: 2. A curve is defined by f(x) = a√√x+b, where a and b are constants. the point (4, 6), determine the…

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Q: Show that xzxx+yzxy = y²Zyy if z = xy + yln(xy)

A: To prove the given result find zxx,zyy,zxy and substitute in the given equation.

Q: Find dy dt || dy dt for y = sin 2 (3nt – 4).

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Q: 29. Σ n=1 n In2 + 4η + 1

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Q: 1 9. Σ n? + 1 n=1 E

A: