Using Disk Method solution, R is bounded by x-axis, y-axis and the line 2x + 3y = 1. This is generated by revolving the region R about the x-axis Draw R and make a sketch of V.

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A: To find the area between the line and x axis.

Q: the integral dx Va? – x? e may use x- educe the integral to a sine and dx= a cose de substitutions…

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Q: Jen would like to use the first week in May to visit one city, and the first week in June to visit…

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Q: Find the area of the blue region. It is the area under the curve. 8 y = 3 x + 1 4 y =7– x 2 4 6 8.

A: This question can be solved using the concept of area under curve.

Q: 2. Find the coordinates of the centre, vertices and foci of the curve with parametric equations: x =…

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Q: m²-m Find S (m1) dm

A: Given; I=∫m3-m-1mdm   As we know that; The Sum rule; ∫fx±gxdx=∫fxdx±∫gxdx The Power rule;…

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Q: In Exercises 1-3, find the general solution of the differential equation specified. dy 3. 2t 1+ 124…

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Q: Calculate ri(t) · r2(t)] and [ri(t) × r2(t)] first by differentiating dt dt the product directly and…

A: Given that,  r1(t)=6t i+9t2 j+5t3 k,  r2(t)=t4k

Q: 11. If f"(x)=-4sin 2.x, f(0)=0and f'(0) =2, find the value of f 4 %3D

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A: topic -exponential function

Q: a1, a2, a3, . be a geometric seq is also a geometric sequence by that af, a3, až, (a) Σ (1- ). (Φ)…

A: topic - sequence and series

Q: If f(x) = 4x(sin I + cos I), find f'(r) -| 4x cos(r)- 4z sin(r) +4 sin(r) +4 cos(r) f'(1) =

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Q: S cos³ 3x dx со

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Q: 4. 7 [fx)dx = - 7, r(x)dx = -7, and = 7. Use these to complete parts (a) through (f). The functions…

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Q: 9. Find the equation of the tangent plane to f(x, y) = x In(y) + x²y+3 at the point (x, y) = (2, 1).…

A: We have to find the equation of the tangent.

Q: Find the value of the limit: lim x→0* sinx+ tan x

A: Given query is to find the value of the indicated limit

Q: A piece of cardboard measuring 11 inches by 9 inches is formed into an open-top box by cutting…

A: A piece of cardboard measuring 11 inches by 9 inches.

Q: Find the derivative of f(x) = log, (7x). (Use symbolic notation and fractions where needed.) df dx…

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Q: Q16. Consider the function z = f(x, y) = x² + 16y? + 4. (a) What is the domain and range of ƒ ?…

A: Given function f(x,y)=x2+16y2+4 As per our guideline we supposed to answer only first three subparts

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Q: Describe the graph of the equation. (8 – 21) i + 13rj r = O It is a plane in 2-space through the…

A: I have appended the formula used in the solution part.

Q: 16. Interpretations of Integrals Determine the position function, s(t), of an object if the…

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Q: 4 dx 16 + x² 2 dx X/x² – 4 2

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Q: (c) in the tank to a height of 1 m above its top. Give a definite integral that computes the total…

A: answer is in next step

Q: Match the vector field with its graph. F(x, y) = xi + 3yj 5 y -6+

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Q: 2n n E(-1)"; n! n=1

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Q: 6 sin z Let f(r) = 6 sin z + 2 coS T Then f'(x) = The equation of the tangent line to y = f(z) at a…

A: Given query is to find the derivative of the function.

Q: Evaluate the integral. 3 if -2 < x< 0 f(x) dx where f(x) | 4 – x² if 0 <x< 3

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Q: Question 7 Find the area enclosed by the curves y=2r², y=2x.x=- and x = 1 A) 45/51 B 65/89 59/76 D)…

A: Here is the solution

Q: Consider the following. dx Let u = 5x3- 1. Find du. dx - np Indicate how the limits of integration…

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Q: Find the particular solution of the following ODE given that y(0)=0 and y '(0)=0: d'y +y=e* dx

A: A Particular solution of the differential equation is a solution of the form y= f(x) , which don't…

Q: Let C1 be the curve with parametric equations x = Cos t, y = sin t – t, where t e [0, ). (a) Find…

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Q: Evaluate the limit sin 9x lim I0 sin 3x

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Q: f(x,y) = 2y3–3y² – 12y+2x2 – 4x+2.

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Q: d d Calculate ri(t) · r2(t)] and r(t) × r2(t)] first by differentiating dt dt the product directly…

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Q: 8- Prove that lim,. -7 (5x – 32) = 3 using the formal definition of the limit. (choose e and 6 )

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Q: Find the value of (5a² – 6)da

A: This is a problem of integration. Based on the formula and concept we will answer the question.

Q: Find the surface area revolve about x-axis at y = x³ from 0 < x< 2 98TT Answer: -sq. units 81

A: The curve y=19x3 from 0≤x≤2 revolved about x-axis.

Q: 7. S(x – 9)7 dx 8. S: r5 dr V3-r6

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Q: The series (-1)"+1 is: n³/2 n=1

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Q: Find the domain of r(t) and the value of r(to). NOTE: Round your answer to two decimal places when…

A: Given :r(t)=cos(πt)i-ln(t)j+t-14k ; t0=15To find : The domain of r(t) and the value of r(t0)

Q: Evaluate the definite integral. ra?/3 xVx6 + a2 dx (a > 0)

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Q: Determine whether the series converges. If it does, find the sum: SUMMATION from n = 0 to infinity…

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Q: Find T(t) and N(t) at the given point. r(t) = (t² – 8)i + tj; t= 8

A: Given,            rt=t2-8i+tj ; t=8To find : Tt and Nt at the given point.We know that,…

Q: ||r(t) × r"(t)|| Use the formula k(t) to find «(t). r(t) = e*i+etj K(t) =

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Q: 2 sin (csc 2x) dx

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Q: at x = 2 for the function below. dx Evaluate y = - 5u? + 4u + 9, where u = 9x2 – 2x + 4 Answer…

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Q: Find S(sin20cose + cos30)d0

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Q: The demand curve for a certain product is given by p(q) = 541 - q. The supply curve is given by p(q)…

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