Consider the following. f(x) = x3 – 12x

Q: f(x) = S, 0 1+x2

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Q: Question 2 ) Consider the initial-value problem y" + 4y = 5 sin 3t, y(0) = 0, y(0) = 3. %3D (a) Use…

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Q: x° 16x6 -24x3 +9 dx

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Q: You have been asked to design a rectangular box with a square base and an open top. The volume of…

A: Concept:  rectangular box volume : The volume of a cuboid is the amount of space it takes up in…

Q: (iv) 15-22 dr. u = (v) S 15 · T/9 – x² dx. 9-z (vi) J +15 da. u=

A: iv) 15x2/sqrt(9-x2) v) 15 pi sqrt(9-x2) vi) 9x/(x2+15).

Q: b) Find the values of a and b so that the unction f(x) = x + ax + b has a local maximum at the point…

A: Given function f(x)=x2+ax+b The local maximum at the point(7, -6) We need to find a and b

Q: Differentiate each function by applying chain rule. Match each item to a choice: y = x(x² + 3)² y =…

A: We have to differentiate following functions using chain rule: y= x(x2+3) 2 y= (4x-10) 4 y=…

Q: The function x2 f(x) 1 - x is decreasing on (0, 1). Select one: O True O False

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Q: +00 Q11: Given that f f(x)dx = 1 where f) - x>0 . The value of c is %3D ISO a) + b) 1 c) - 1 d) 3

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Q: Find all the local maxima, local minima, and saddle points of the function. f(x,y) = e 2x2 + y? - 8x…

A: To find out all the local maximum, local minimum and saddle points.

Q: Find the equation of the line tangent to 2e"y = x + y at the point (2, 0). Write the equation in…

A: Given query is to find the the equation of the tangent to the curve.

Q: 4 Which formula would be used to calculate the trapezoid approximation of L dx using five…

A: We have to use trapezoidal rule. Option B is correct.

Q: 4. y = x, y = 2x, and x + y = 6 (Answer: 3 s. u.)

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Q: 9. Oil spilling from a ruptured tanker spreads in a circle on the surface of the ocean. The area of…

A: Oil spreads in circle on surface of ocean. Area of circle is A=πr2.…

Q: 1. Evaluate the following integrals. 24 - 44 dy 2+ 49 C.

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Q: 2. Find the second derivative for the following set of parametric equations. = t° – 4t3 y = t?

A: We have to find the second derivative of the given equation.

Q: sin(x²) ate lim 1+0- e2r – 2x – 1°

A: zero by zero form then apply L hospital rule

Q: Consider the differential equation r'y" +3ry'-3y 2a - 3r. of variation of parameters to solve the…

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Q: a) Use the Second Derivative Test to find the local extreme values of the function f(x)=(x^3+27)^4.

A: We have to use the Second Derivative Test to find the local extreme values of the function.

Q: Find the curve's unit tangent vector. Also, find the length of the indicated portion of the curve.…

A: This question can be solved using the concept of unit tangent vector and length of vector curve.

Q: Solar Power More and more businesses and homeowners are installing solar panels on their roofs to…

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Q: Question 4 Each side of an equilateral triangle measures 3cm, with a possible error of 0.1cm. Using…

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Q: The power series representation of 1 f (x) = 5x + 4 is: 5 25 125 x+... 256 | - 4 16 64 125 x+... 256…

A: In this question we have to find series form of the function.

Q: 2л + 3 dx 4г2 — 4х + 5

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Q: (iii) Extremum point(s), (iv) The interval of concavity, (v) Inflection point.

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Q: You are stationary on the ground and are watching a bird fly horizontally towards you at a rate of 2…

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Q: Activity 3: 1. ſx²dx 2. SVx?dx 3. S(x³+x²)dx 4. SVx*dx 5. fx-2dx 6. S tan?x dx 7. S(1 – cos u)du 8.…

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Q: What are the local extreme values of the function f(x) = x' – 3x + 2? a. None of these. O b. Local…

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Q: Use Intermediate Value Theorem to explain why the function has a zero in the given interval. [0. 1]…

A: Given problem:- Use Intermediate Value Theorem to explain why the function has a zero in the given…

Q: Sketch the region bounded by the given lines. Then express the region's area as an iterated double…

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Q: Use differentials to estimate the relative error in the lateral surface area of a right circular…

A: Relative error

Q: Find and sketch the domain for the function. foxy) = - 25) ( - 4) Find the domain of the function.…

A: function f(x,y)=(x2-25)(y2-4)

Q: Find all the second order partial derivatives of the given function. f(xy) =xy° +y¢* +5 O A. f = 2x,…

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Q: Evaluate: 1) [x.e*c

A: We will solve the integration using integration by parts.

Q: Cross-product of vectors   ⟨2,−1,3⟩×2⟨4,2,1⟩=?

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Q: Find the curve whose slope at any point (x,y) is 6x^2−2x−5 if the curve is required to pass through…

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Q: Change the Cartesian integral into an equivalent polar integral. 3 0-x SS (P+y?) dy dx = J JO dr de…

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Q: 2. If the acceleration function of a certain particle is given by a(t) = sech () tanh () – ei, find…

A: Given Data: a(t)=secht2tanht2-et2 Solution: Let v(t) be the velocity. We know that, dv(t)dt=at…

Q: Which of the following is the particular solution of a nonhomogeneous differential equation…

A: Here, given that: yc=c1x2+c2x3⇒y1=x2, y2=x3 And, u1=2x-3x2, u2=2x+3

Q: .5 dx Vx4 – 2x2 + 1 b. 3

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Q: n3 + n? ) Σ 00 (n – 1)! n=1 2n + 3 n2 In n n=1

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Q: 2. Suppose a wire three feet log is to be cut into two pieces, with each piece to be formed into a…

A: 2) as per our norms we have to write one question at a time kindly repost remaining questions.

Q: 2 cosx+3 cosx=2, 0Sx<27

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Q: Jse any method to determine if the series converges or diverges. Give reasons or your answer. 9n 2…

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Q: Find the Taylor polynomial of order 3 generated by fat a. f(x) = x2 +x+1, a=2 O A. P3(x) =7+5(x- 2)…

A: f(x)=x2+x+1f(2)=4+2+1 =7f'(x)=2x+1f'(2)=4+1 =5f''(x)=2f''(2)=2f'''(2)=0

Q: Find and sketch the domain for the function. sin (xy) f(x,y) = y - 36 Find the domain of the…

A: This question is related to Functions, we will solve it using given information.

Q: 4 y = ,x = 1,x = 4, and y = 0 is revolved about the y – axis. (Answer: 24n c. u.)

A: This question is based on finding volume of solid.

Q: 3. Out of frustration, Maxine throws a stone into a river. This caused ripples in the form of…

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Q: dy + 7z = 5 5 – 72

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Q: In a race, Molly starts running from rest at a constant acceleration of 3 m/s². She is running in a…

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