Do the following tasks using Mathematica. Given, f(x) + x? g(x) = T sin(x) %3D (a) Plot the above functions in a single graph for -<* < (b) Find the limits of the integration for the the area of the region enclosed by f(), g(x), x = - and x = 4 Hint: i) Solve the equations to find the intersections. ii) Visualize the plot and the boundary regions. 4 (c) Finally, do the integration to find the area.

Q: 3. sinx tan x + cos x

A: We can simplify the expression as below.

Q: Which of the following is not true? (A) - |f(x) dx- J8 (x) dx B) 8 (x) dx C) (x)dx=k (D) O fas(3))dx...

A: some properties of the integration are given, we have to find the not true statement.

Q: B: Evaluate the integral: TUTO (x + 1)-/2 (x – 1)5/2

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Q: attached picture please attached

A: Topic:- derivatives

Q: - / 4(1-)esc2(1– y)dy

A:

Q: general function M(x, y) or N(x, y) so that equation is exact.

A: We will find the function (general). 

Q: 3. The population P of a certain small town t years from now is predicted to beP(t) = 35000 + %3D 10...

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Q: x(/x+y) +у) — 8 — ху

A:

Q: Q/ Find the domain and range of the following functions メー」 y= 2y= メ+ 3+13 メー/3 3- 1,

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Q: 4) y -2sin x, y=-2cos x, X -- 6' 6.

A: Since you have posted multiple question in this question which re not interlinked so i have solved f...

Q: A function f(x,y) is homogeneous of degree 7 in x and y if and only if, __________.

A: Given problem is solved below.

Q: and horizontal lines), without performing the integration. (c) Write down the integrals with their l...

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Q: 3.b) Evaluate the DE * 3x(xy – 2) dx + (x³ + 2y)dy = 0

A: Given that: 3x(xy-2)dx+(x3+2y)dy=0

Q: Homogenoys Equations: Evaluate the DE xdy+(2y-x)dx=0

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Q: 2メー7 f xス」

A:

Q: 1. Consider a rectangle with perimeter 28 (units). Let the width of the rectangle be w (units) and l...

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Q: Beth is filling a small backyard pool with a garden 647. hose. The pool holds 30 gallons of water. A...

A:

Q: All parts of this problem refer to the function below. y = (9+ 6x)²/¤ dy a) Use logarithmic differen...

A: We have to find derivative

Q: 2. 3t2 (t3 + 4)5 dt 3. 5x2 1- х3аdx

A:

Q: By using substitution method, evaluate: (a) dx (e3x+x3)3 (In x) dx (b) 4x

A: To evaluate the integral.

Q: What is the equation of the curve whose slope at the point (x, y) is 3x² if the curve is also requir...

A:

Q: P3.B: At any point of a curve y =f(x), y" = 6x + 4. If the curve passes throurh the points (1, 0) an...

A: y"=6x+4auxilary eq m2=0⇒m=0,0y=(c1+c2x)e0x⇒ y=c1+c2xparticular integral PIPI= 6x+4f(D)=6x+4D2=1D1D(6...

Q: 14х10+8 еx F (x : 4 x' + 13

A: Given: fx=14x10+8ex4x+13

Q: Consider the series > 5e". n=0 a. The general formula for the sum of the first n terms is Sn (5e( 1-...

A: This is a problem related to series calculation. Based on the simplified terms it was observed that ...

Q: A wound is healing in such a way that t days since Monday, the area of the wound has been decreasing...

A: topic - application of derivatives

Q: A car is travelling at 72 km/hr. At a certain instant its brakes are applied to produce a constant d...

A:

Q: 10 – 2x6 dx

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Q: Find thlength of the curve.  Y=1/6(x^2+4)^3/2, 0<x

A: We have to apply arc length formula to solve the problem

Q: Let f be a differentiable function. If f(50) = 378 and f'(50) = 6, use a linear approximation to est...

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Q: .A: The integral of the following function: In(sin² x) dx tan(x) ay be expressed as: A In®(sin x) + ...

A: Topic:- integration

Q: Question 14 Which of the following is an equation of the parabola with the following properties: ver...

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Q: 1.Determine if the following statements are mathematical or not. Provide solution.

A: Given that:                      

Q: y = Vx (x – 1) u = i + ī + 4/15 y = f (r² + t + t')

A:

Q: 6. PARTIAL DERIVATIVE OF MULTIVARIATE FUNCTIONS Find and for the following function. z* sin (y") + x...

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Q: 2. x'dy+(2xy-y'dr = 0 Let the substitution y=2; y= vx, dy=vdx+ xdv

A: x2dy+2xy-y2dx=0

Q: determine the most general function M(x, y) or N(x, y) so that equation is exact.

A: We have to find M(x, y) Or N(x, y). 

Q: Agree. function always exist? Justify: Disagree 2. Does the limit of a

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Q: 1. Find the area under the curve y = 9- a2 over the interval[0, 3] using right end point approximati...

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Q: 57 37 Convert the point (p, 0, 4) = ( 5, 3 to Cartesian coordinates. Give answers 4 - as decimals to...

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Q: 3. Solve the differential equation by variable separable method (1+ y") (3a² + 6) dy 9- dr 13 + 6r

A: dydx=91+y23x2+6x3+6x  

Q: Calculate the Taylor polynomials T2(x) and T3(x) centered at x = 0 for f(x) = sin(x). (Use symbolic ...

A: We will find the T2(x) and T3(x) for the given function.Below find the solution in the image.

Q: 1 The function is equivalent to the series: 1-2t Select the correct response: 3 5 -1 -t--t2 2 t3 + ....

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Q: (a) y = -T (b) y = 2x° + 3x (c) y = x² + 5x 7 (d) y = x(x - 1) %3D -

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Q: The stopping distance for an automobile (after applying the brakes) is approximately F(s) = 1.1s + 0...

A: Given:- The stopping distance for an automobile (after applying the brakes) is approximately F(s) = ...

Q: y'dx- (gy + y* }ty = 0 1. Let the substitution v=2; y= vx; dy=vdx + xdv

A: We have to find solution of given differential equation.

Q: An investment firm expects the price of the Campbell’s Soup Company stock to increase via P(t)  =  P...

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Q: Solve using homogeneous differential equation y'dx- (xy + y° kty = 0 Let the substitution y=? 2; y=v...

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Q: Use the Integral Test to determine whether the infinite series is convergent. 16ne-n? n=6 Fill in th...

A: ∑n=6∞16ne-n2

Q: Sketch the region bounded by the graphs of the equations and find the area of the region. y = cos x,...

A: The region is bounded by y=cos x and y=2-cos x, 0≤x≤2π

Q: 2. lim f(x) and lim f(x) if f(x) = V4-x2 %3D X-2+ X→2- х-2

A: