Answer all questions in the space provided. Show ALL your steps in your calculations. Answer in complete sentences when necessary. Answer the following question by using the given information to analyze: Let a=2, b=50, c=1, d=8 and e=15 is given by the following function: 10- 2x2–50 8 (x)=- x2+8x+15 x=-3 Find the following analyses of the function: リー2 1. Determine the domain -10 10 2. Determine the range 3. Determine holes 22- 30 y= r+ 8x +5 Determinee arumntoter

Q: TE: Enter the ezact answer. y =z²+3 y =r 3

A: given is   region bounded by               y=x and y=x2+3              x=-1 to…

Q: Describe the graph of the equation. r = (5 – 21) i + 11tj O It is a plane in 2-space through the…

A: In this question we have to describe graph of equation.

Q: Solve for the volume of the solid generated by rotating the plane bounded by the equations below…

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Q: Find the area bounded by the curve y=x^2 − 4, the lines y = 0 and x = 4

A: The graph is shown below:

Q: 5- S(tanx + secx)² dx

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Q: Find dy/dx: а. y = cos t dt

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Q: Find the directional derivative of the function at P in the direction of v. f(x, y, z) = xy + yz +…

A: Given,            fx,y,z=xy+yz+xz , P8,9,-8 , v=16i+j-kTo find : Find the directional derivative of…

Q: Use cylindrical shells to find the volume of the solid generated when the shaded region is 1…

A: Let's find.

Q: Ti al Write step-by-step solutions and justify your answers. Solve the initial-value problem y" +y -…

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Q: Find the total area enclosed between y = r and y = x over the interval [-1,5]. NOTE: Enter the ezact…

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Q: Find the limit. NOTE: Enter the answer using round brackets. t² + 8 1' lim t→+∞\ 9t² + 10't (?, ?)

A: We can solve this as follows:

Q: The auxiliary equation of the homogeneous linear equation y" – 24y' – 16y = 0 is m? – 24m – 16 = 0…

A: Given differential equations y''-24y'-16y=0

Q: 3. Supply the missing integrand and limits of integration. 61y drdy fip (b) 62y dydz =- dr

A: Solve it.

Q: For Item # 9 - 10: A company manufactures fuel tanks for automobiles. The total weekly cost of…

A: As per our guidelines we can answer only 1 question so kindly repost the remaining questions…

Q: Provide a step-by-step solution to the following differential equation (linear quation) y' = x3 -…

A: I am attaching image so that you understand each and every step.

Q: Question 1 Use the First Derivative Test to find the local maximum and minimum values of the…

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Q: Given the following optimization problem: max(500-q)q-50q q*=50 O True O False

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Q: 18+21x-x2 Resolve into partial fractions (x-5)(x+2)²

A: Solving the problem by finding the expression as defraction.

Q: C is polygonal path from (0, 0) to (3,0) to (3, 2); the sur- face is f(x, y) = 2x +y

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Q: QI) Evaluate the integral dx dy using polar coordinate

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Q: A spring whose natural length is 13cm exerts a force of 37N when stretched to a length of 18cm. (a)…

A: Given that the spring whose natural length is 13cm exerts a force of 37 N when stretched to a length…

Q: cting with water in an acidic solution at a particular temperature, compound A decomposes into…

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Q: Find the domain of r(t) and the value of r(to). NOTE: Round your answer to two decimal places when…

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Q: 16. Graph the line determined by the two points, and find the slope of the line: (-1,2), (7,8)

A: slope of the line passing through the point  (x1 , y1)  and (x2,y2) is m=y2-y1x2-x1

Q: Consider the differential equation y" – - 1ly" + 28y = 0 %3D

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Q: n(x) = csc²(;2) Select the correct response: 1 1 CSC + cot(5) - 1 sec"(5e) tan(-e) csc²(-x) cot(r) 2…

A: We have to find the derivative of the above equation.

Q: Find the total area enclosed between y = x and y = a over the interval [-1,5]. NOTE: Enter the exact…

A: The region bounded  by y=x3 and y=x over the interval -1,5

Q: The substance's amount at time t may be modeled by an exponential function. Substance X has an…

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Q: (x² + 6)cotx 3 – cosxcscx Find f'(x) when f(x) 6cotx – 3(x² + 6)csc²x + 2xcot?x f'(x) = (3 – cotx)?…

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Q: Question- Let R be the region bounded by x= y-25, and x= 1. Then draw the region and. evaluate the…

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Q: Consider the differential equation y" – 11y" + 28y' = 0 Write the auxiliary equation of the given…

A: Given a higher order differential equation.

Q: t2 + 5 1 lim →+∞\ 9t2 + 10' 2t (?, ?)

A: Given

Q: Question 7 of 10 f (x) = x – 6x² + 9x - 2 Select the correct response 2.x2 + 12x – 9 - 6x - 12 372 –…

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Q: Consider the differential equation y" – 11y" + 28y = 0 Write the auxiliary equation of the given…

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Q: dx 1-S; 4+x2

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Q: 5x 8. 10e dx

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Q: dx 1- S 4+x2

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Q: 2- fx³e-2x* dx

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Q: 4. Sdx

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Q: d d Calculate ri(t) · r2(t)] and [r1(t) × r2(t)] first by differentiating dt dt the product directly…

A: We have to find derivative

Q: Suppose car A is heading south at 85 km/h and car B is heading east at 90 km/h. Both are headed for…

A: Consider

Q: What is the derivative of 3x+5?

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Q: The base of a solid is the region in the xy-plane bounded by the curves a = -y² + 2y + 145 and x =…

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Q: ! Solve the boundary-value problem y"+ 9y = 0, y(0) = -3 and y(a/3) = 2.

A: To solve the given differential equation.

Q: Find the derivative of the given function. Fill the missing expressions. Use logarithmi…

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Q: The functions yi = e linearly independent solutions of the homogeneous differential equation x and…

A: Two solutions of a differential equation is said to be linearly independent iff their wronskian is…

Q: 3x+1 7. 9e ax

A: The given integral,       ∫9e3x+1dx

Q: If a > b, it is possible to have log,(a) < log,b). (As usual with logarithms, a and b are positive…

A: From the rule of logarithmic inequality, If x &gt; y , then logax&gt;logay if x, y&gt;1 If x &gt; y…

Q: Activities in Logarithmic Differentiation Find the , evaluate for given x – values dx' (x-2)²/x+1 y…

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Q: Problem 5. Which gives the Laplace transforms of the given time-domain function? In [(s - sqrt 2)(s…

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