Sketch the function  f(x)=-x3-3x2

Q: Problem 7 Proof that if lim f(x) exists then it must be unique i.e., x→a if lim f(x) = L and lim…

A: limx→af(x) exitsif limx→af(x)=L and limx→af(x)=M then L=M

Q: True or False; The definite integral 3 [²²x + ²e¹)dx 5 is equal to 3 5 J-1 Select one: O True O…

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Q: Calculate the area of the parametric surface given by: r(u, v) = 2 sin u cos vi + 2 sin u sin vj + 2…

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Q: explain

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Q: find f f'' (x) = 2 + cos (x) , f (0) = 7 , f (pi/2) = 2.   f (x) =

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

Q: Compute the integral dx.

A: As we know that ∫xmdx=xm+1m+1+C see below the answer and calculation

Q: Solve the given IVP using Laplace Transforms. Solve for x(s) and STOP! (Express x(s) as a single…

A: Given IVP is x'' + 9x = cos3t,  x0=0,  x'0=2

Q: Evaluate € 11/² 2xz dV where E = {(x, y, z) | 2 ≤ x ≤ 3, x ≤ y ≤ 2x, 0 ≤z<x+3y}

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Q: Problem3 Find a curve in the xy-plane passing through the point (1, 2) and for which th normal line…

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Q: find y' at y = f(x) уч x 2 x ² y - =1

A: Given function is :-x2y-y2x=1To differentiate it, use :-ddxu(x)v(x)=u(x)ddxv(x)+v(x)ddxu(x).and…

Q: 19. For a given function, f(r)=³-152² +48x+2. (a) Find the interval(s) on which is increasing. (b)…

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Q: Question 1 Consider the points A(2,-1,0), B(3, 0, -2), and C(0, -3, -1). (a) Find the equation of…

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Q: 9. If = 1, 4, 5) and W = (2, -3, 1 V ( − w a) 3-2W b) |v|

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Q: Find the sum of the series: n=0 2-1 (-1)"64"- n!

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Q: The data given in the Table below is produced from a Linear Difference Equation model of the form: Y…

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Q: Find the indefinite integral. (Use c for the constant of integration.) [ (42³1 + (4t³i + 14tj…

A: We need to find integral.

Q: Set R be the region defined by √2² +²³² ≤4 and let f(z,y) = 1²-22+ y². Find the global maximum and…

A: The region R given is: x2+y2≤4y≥x

Q: Find the area of the surface generated when the given curve is revolved about the given axis. 7 y =…

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Q: 08 06 04- 02- }} ye y=0x=y² 02 yer* dxdy = 36 38

A: To switch the order of integration and then evaluate the value of integration.

Q: a 3. Sketch the graph of +₁ f(₂)=1₁ continous function & $²(2)=0, the point (2,1) is 2 £ is…

A: Let's solve.

Q: Find all solutions of the equation in the interval [0, 2π]. 2cos2xcosx-2sin2xsinx = 1 Write the…

A: Here, the given equation is: 2cos(2x) cos(x)-2sin(2x) sin(x)=1⇒cos(2x) cos(x)-sin(2x)…

Q: Set up integrals To find the area of the regions between the curve of y=4 cos x and the x axis for 0…

A: The Solution is given below

Q: The definite integral is equal to [²3x 3xdx Select one: O none of the others O 3 lò O3 lò xdx +3 lit…

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Q: Question 1 Let a = 2i - 3j + 2k and b = i - 2j - k. a) Determine whether the vectors a and b are…

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Q: (b) Use the Fundamental Theorem of Calculus to evaluate the integral 8 x-6 So ²x+8 dx

A: Use fundamental theorem of calculus to evaluate the integral.

Q: The value of the definite integral 3 [² (3x² Jo 0 is (3x² - 2x + 4)dx

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Q: 20. The graph of the first derivative f' of a function f is continuous on (-∞, ∞). -1 f (x) 2 3 (a)…

A: Note:- As per our company guidelines we are supposed to answer only first three sub-parts. Kindly…

Q: Find the derivative using logarithmic differentiation. x(x + 4) (5x + 1)(3x +7) (Express numbers in…

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Q: The equation of the plane that passes by P(2,0, -1) and that is perpendicular to the line x-5 2-y…

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Q: The slope of the tangent line to a curve is given by f'(x) = 7x² + 9x - 8. If the point (0,5) is on…

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Q: J (2) Ten thousand dollars is invested at 645 intrest Compound Continously. → when will the…

A: We can find the required time as below.

Q: Find all solutions of the equation in the interval [0, 21). 2 cos²x=2+ sinx Write your answer in…

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Q: 5. (8 pts) An isosceles right triangle is as shown in the figure. The leg is increasing at a rate of…

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Q: Solve the given IVP using Laplace transforms. x" - 2x + x = 2tet x(0) = 0, x'(0) = 0

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Q: lim 0-4 In[(1 + h)² + 1] - ln(2) y

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Q: True or False: We have Select one: True False -8 √xdx = 64 3

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Q: Question 2 Consider the point P(-2, 1, 4) and the vectors a = and b=. (a) Find the unit vector u…

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Q: 10 [.. 4 √x + 2dx = [Please enter your answer t format(For example: 3.14)]

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Q: 3. The radius of a sphere ball is measured at r= 25 cm. Estimate error in the volume and surface…

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Q: 6 Find an equation of the line to the curve Y= √x that is parallel to the line 6x +Y=1. Y =

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Q: calculate the derivative below using the definition of derivative. f(x)=e^[cos(x)]  a = pi/2

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Q: For the function f(x)= (8+2x, if x5) A) use definition of continuity at a number (3- step test) B)…

A: Concept: These are the three requirements for continuity: 1). The equation for the function is x =…

Q: f(x) = e6x + e−x find the locacl minimum value of f

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Q: Write a recursive formula for the arithmetic sequence an given below. an= and a1= 10,19,28,37,46,…

A: To write a recursive formula for the arithmetic sequence given below.an=? and a1=?10, 19, 28, 37,…

Q: Find | 22 x²z ds, where C is the line segment from (0,4,-6) to (2,9,-5)

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Q: Find all solutions to the equation. tan 0-1=0 Write your answer in radians in terms of it, and use…

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Q: Evaluate 3 [²^{²} + √x² − ² + ³x² − ²) dx = x None of them 21.466 2.1664 -2.1646 -21.664 21.664…

A: Given problem:-

Q: 2 y=0x=y f(x,y) dxdy =

A: Solution given below

Q: Find the average value of f(x) = Enter the exact answer. fave = x (6x² + 5)² over the interval [0,…

A: Avg value is given by below

Q: Brine containing 3 lbs per gal of salt enters a large tank at the rate of 2 gal/min and the mixture…

A: Concept: Let z represent the amount of salt in the tank at time t, where t is given in minutes…