Find the most general antiderivative of the function f(æ) = 3e* + 6 sec² x. Answer: F(x)

Q: 3. The following statements indicates the use of descriptive statistics EXCEPT A. Last school year, ...

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Q: Find the critical numbers of the function. (Enter your answers as a comma-separated list.) h(x) = si...

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Q: ii. (x + y)dA Where R = {(z, y)|1 < x² + y? < 4, x < 0}

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Q: write the slope-intercept forms of the equations of the lines through the given point parallel to t...

A: This is a question related to equation of line and slope passing through particular point.  General ...

Q: Find the volume of the solid obtained by rotating this region about the line x = 3.

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Q: dt 七

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Q: Find parametric equations for the tangent line to the curve with the given parametric equations at t...

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Q: equations for the line segment that joins P to Q. P(0, 0, 0),    Q(−3, 8, 6) vector equationr(t)=   ...

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Q: Sketch the level curve for f(x, y) = 36 – 9x? – 12y2. '36— 9х2 —

A: Given function f(x,y)=1236-9x2-12y2

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Q: Consider the following. y = tx2 + t8x Find dy dx dy dx dy Find dt dy dt

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Q: dx Jx +

A: Given that: ∫dxx+x3

Q: 1. Consider the region bounded by y = x and y = vVa, shown below. Find the volume of the solid obtai...

A: Volume=13π15 cubic units

Q: 2w +x + 2y +z = 6 -9x + 9z = 18 - 5z = -13 - 3y = 4

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Q: Divide the numerator and thế denomih by lim 9. + 2

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Q: Solve the linear differential equations (D5- 2D3- 2D²-3D-2) y =0

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Q: 4 dx

A: Use limit comparison test and p series test

Q: lim (x,y)→(0,0) f(x, y) to be along the path Y = x. Based on the table of values, enter what you bel...

A: Based on the table values we have to find the limit value.

Q: Find the area of the region bounded by the graphs of the equations. Use a graphing utility to verify...

A: Apply integration to find the area of the region

Q: not 2022-02-20 5.44.12 PM.png Discard edits Save Find the time required for an object to cool from 3...

A: Use integration formula

Q: f(x) = 3x² – 6x+1, taking the sample points to be point and a = 0,6 = 3, and n = 8. %3D Find the exa...

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Q: For items 25 - 30, consider the frequency distribution of the Age of Employees of MTF Inc. Complete ...

A: Given:   Data with table is given

Q: valuate and solve the linear differential equation (D5 - 15D3 + 10D2 + 60D - 72) y = 0

A: Given: (D5 - 15D3 + 10D2 + 60D - 72) y = 0

Q: (c) When will the rock hit the surface? We note that the rock will hit the surface when its height a...

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Q: 3. j. lim f(x) k. lim f(x) X→3+ 3. 1. lim f (x) I m. lim f(x) x→3 y f(x) n. lim f(x) о. f (3) X→+∞

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Q: At what points is the following function continuous? 2-4x-5 x#5 f(x) = X-5 6, x= 5

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Q: The graph of y = f(x) has the following features: f(– 2) = - 2 lim f(z) = 2 %3D H -2- lim f(r) = - 1...

A: Given : f(-2) = -2   

Q: Problem 2. A Bernoulli differential equation is one of the form dy + P(x)y= Q(x)y" (*) dr Observe th...

A: First order differential equation : Consider the first order differential equation             dydx+...

Q: Suppose that f and g are functions h'(1). f(x)g(x) h(x) %D f(x) – g(x) | h'(1) = %3D

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Q: Consider the following. y = tx2 + t°x dy Find dx dy dx dy Find dt dy dt II II

A: y= tx2+t9x  1) find dy/dx  2) find dy/dt 

Q: 1 ao et/2 dt = 0.50 2 An e-1/2 cos 2nt dt = 0.504 1+ 16n? 8n b, = et/2 sin 2nt dt = 0.504

A: a0 = (1/π) ∫0π e-t/2 dt , put -t/2 = x , dt = - 2dx Using formula ∫ et dt = et + c a0 = (1/π) ∫ ex (...

Q: Find an equation of the plane. the plane through the point (9, 2, 5) and with normal vector 3i + 5j ...

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Q: Due to depreciation, the value of an automobile t years after purchase is f(t) = ((900 + 6t / 1+0.5t...

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Q: 1 cosØ dø (7-sin²Ø

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Q: 1 1 xa(1 - x)*dx = | x*(1 – x)ªdx Þ(1 – x)ªdx

A: Given: - The  equation is, ∫01xa(1-x)bdx=∫01xb(1-x)adx, That if a and b are positive numbers. To pro...

Q: Solve the linear differential equations dx= 4+5y =D 8 sin x when %3D x-0, y=0 y'=o Find y when x = T

A: See the details solution in below

Q: 2x +1

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Q: If the derivative d (instead of ) exists at a point and = 0, then the tangent line at that point is ...

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Q: Find the derivatives for the following function: a. Z-f(x, y)-6e*+4x*y- 8lny ze Find the partial der...

A: z=6ex+4xy-8lny firstly differentiate partially w.r.t x∂z∂x=6ex+4y(1)-0∂z∂x=6ex+4y

Q: The equation of the plane through the point (2, 5, 7) that is parallel to the line 7(t) = 3î + 2 – 2...

A: Explained below 

Q: Find the DE of each of the following by eliminating the arbitrary constants. y = ln tan(x – A)+B

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Q: 12) sin-1 -1 14) tan 0 V3 16) sin-! |

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Q: 2. Answer C/DC a. lim f(x) x2 b. lim f(x) X-2+ c. lim f(x) -3 -2 -1 -1 X-2 d. lim f(x) -2 X-5 -3 e. ...

A: limx→a f(x)=L if and only if limx→a+ f(x)= L=limx→a- f(x).

Q: c) So lz² – 4| dx sin a d) L', dx da e) J JetItya

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Q: Use the Shell Method to calculate the volume of rotation, V, about the r-axis for the region underne...

A: Here, the region is bounded by the curve: y=(x-2)13-2, x-axis and 10≤x≤218  

Q: り のx + ex t 1tx - dx x* + 2x t 5

A: (i) ∫dxx=ln(x) (ii) ∫dxx2+a2=1atan-1(xa) (iii) ∫xndx=xn+1n+1, for any real number n.