Suppose (S,d) is a metric space. How can we prove that S is open

Q: Evaluate the given integral by using three terms of the appropriate series. 0.7 0 sinx²dx 0.7 S…

A: let  J=∫00.7sinx2dxwe know series of sinx is sinx=x-x33!+x55!

Q: Use the Ratio Test to determine if the following series converges absolutely or diverges. nº Σn=1…

A: use ratio test to check the convergence of series

Q: Prove formally using the e-6-criterion that the function f(x)= [x² +1, 12, is continuous at x = 1 if…

A: We have to show that function is continuous at x=1.

Q: Suppose that the variables x and y are related by the implicit equation V = -3.4x 1.3 ln(x)+2.4y—…

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Q: "OIL SPILLS In calm waters, the oil spilling from the ruptured hull of a grounded tanker spreads in…

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Q: Q3. Find the equation of the tangent line to f(x) = x³ at x = 5.

A: f(x)=x3f(5)=53f(5)=125Point of tangency is: (5, 125)f'(x)=3x2Slope of tangent line:m=f'(5)m=3(5)2…

Q: If f(x) = ln(x), then the estimation of the area under the curve y = f(x) between a=1 and b = 2 with…

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Q: Consider the function f(x) = 4-6x², -5 ≤ x ≤ 1. The absolute maximum value is and this occurs at x…

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Q: α. 3 n Σ 4 n=1 |

A: Since you have asked multiple question, we will solve the first question for you as per our guide…

Q: Find the derivative of sec(x)x²(x + 7)5. Answer:

A:

Q: Let f(x) = e-(5x³+5x+5) The derivative of f is f'(x) = = 0 An equation for the tangent line to the…

A: As we know the slope of the tangent line to the given curve is equal to the derivative of the given…

Q: Find the volume of the solid obtained by rotating the region in the first quadrant bounded by y =…

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Q: Perform vector operations. Let Q=(4,1) and S = (2, -7). Find the component form and magnitude of the…

A: Given query is to find indicated vector and it's magnitude.

Q: List the one critical number of the following function. g(x) = x¹/³ — x−2/3

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Q: For the following telescoping series, find a formula for the nth term of the sequence of partial…

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Q: At which of the following polar coordinates is/are the tangent line(s), on the polar curve T = e,…

A: NOTE: Refresh your page if you can't see any equations. . the given curve is  take derivative

Q: 3 L²T³ « 1 (12x3 - 27x²y²) dy dx

A: Given integration is ∫01∫13(12x3-27x2y2)dydx

Q: 4. Choose the statement below that can NEVER be true. O A. I f(x) > 0 B. | f(x) | 20 OC. If(x) < 0…

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Q: The equation of the plane that passes through the origin with the normal vector < 2, 3, 4 is: 2x +…

A: As we know Equation of plane passing through point x1,y1,z1 and normal vector A,B,C is…

Q: -S dx x² + 2x + 5

A: Question no. 29,Giiven,             ∫1x2+2x+5dx

Q: ƒ(x) = √x. The local linearization of ƒ at 16 is L16(x) = Yo + m(x − 16), and yo= ere m = ng this,…

A: We know that  La(x) = f(a)+f'(a)(x-a). By using thus we find local factorization of f(x).

Q: curve y = x + 3e at the point (0, 3). y = Find the equation of the tangent line to the ₂4 0

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Q: Given g is a solution to the differential equation f (t, y), with initial condition g (0) = 1, find…

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Q: Find the magnitude and direction angle of a vector. Find the magnitude and direction angle of the…

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Q: At which of the following polar coordinates is/are the tangent line(s), on the polar curve = eº,…

A: NOTE: Refresh your page if you can't see any equations. . the given curve is  take derivative

Q: Suppose g(x) is a constant function such that g(x) > 0 for all ï. The limit 4x² + x g(x) - 2x is…

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Q: Find the absolute maximum and minimum of f(x, y) = 5x +y within the domain x² + y² ≤ 16. Please show…

A: The given function fx, y=5x+y. We have to find the absolute maximum and absolute minimum of fx, y in…

Q: The parametric equation of the line that passes through the point (3, 2, 1) and parallel to the…

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Q: Evaluate the given expression. Take 0 A = 2 1 -1 0 -1 AT + 3CT 000 and C= 1 1 -1 1 -1 -1

A: I am going to solve the problem by using some simple calculus to get the required result of the…

Q: if ƒ'(x) = F(x) Then ſf F(x) dx = f(t) — ƒ(0) Select one: O True O False

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Q: reu 5. Volume with respect to time when r = 15 cmnco All

A: Please see the below picture for detailed solution.

Q: Find the absolute extrema of the function f(x, y) = x² + y² +x+y+1 on the domain defined by x² + y²…

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Q: Mike's company makes $4.32 per box shipped to the customers. Mike has already paid $276.50 for…

A: We have to find the value of shipped boxes.

Q: How many non-zero derivatives does f(x) = 3x³ + 7x² 9 have? Find all non-zero derivatives: f'(x) =…

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Q: 3. Determine the following for the vectors: p = [2, 3, 6], q= [1, 5, 4]. a) p - 2q b) p q c) px q d)…

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Q: Find a parametric representation for the surface. the plane that passes through the point (0, -1, 3)…

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Q: 2. The radius of an adjustable right circular cylindrical tank is increasing at a rate of 2 cm/hr…

A: Given :A=2πr2+2πrh

Q: Let F(x)= 4x-5 4x + 4 and G(x)=x+1. Find the domains of the compositions Fo G and G o F. X-1' Domain…

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Q: 37. r(t) = (te', e¹, √√2t), -5 <t<5 GA0 01220

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Q: If f(x) = 5 + 2x - 3x², find f'(2).

A: To differentiate the given function f(x).

Q: 2. Explain what it means for vectors to be each of the following: a) equal b) opposite c) collinear

A: A) equal vector

Q: Write each vector in component form. |p| = 85, 60° 0 85, O 85√3 2 0 O 85√3 2 85√3 85 2 3 V

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Q: f(x) = 2x³x² - 10x + 5 (2x - 1)

A: Let  us divide the  polynomial by given factor

Q: b) How large rebate should the company offer to a buyer, in order to maximize its revenue? $ c) If…

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Q: Set up an integral to find the area A of the region enclosed between f(x) = 0.6x² +4 and g(x) = x…

A: Given

Q: Find the point on the graph of f(x) = x² in which the tangent line is y = 4x - 4

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Q: Evaluate the given function by using three terms of the appropriate Taylor series. √15.7

A: Solution: The Taylor series of the function f(x) = x centered at x=a is given by:…

Q: The Tubular Ride Boogie Board Company has manufacturing plants in Tucson, Arizona and Toronto,…

A: a) yes Tucson plant capacity = 620 per week Toronto plant capacity = 410 per week Let number of…

Q: A projectile is shot from a cannon. The fixed parameters are the acceleration of gravity, g = 9.8…

A: Given: g=9.8 m/s2v0=500 m/sfθ=v02gsin πθ90 meter

Q: EXCERCISE 7 1. Find the Maclaurin polynomials of orders n = 0, 1, 2, 3,and 4, and then find the nth…

A: I am going to solve the problem by using some simple calculus to get the required result of the…