NUMBER 3 CLEAR AND SIMPLE

Q: Find the area bounded by the curve x = y² + 2y and the line x = 3.

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Q: c4 So So (6x² +9y²) dx dy

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Q: - 6 = ₁6 -X

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Q: ¹In(1 + x) -dx X

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Q: For the function f(x,y) = √y² + 5x², find f(2, - 5), f(− 1,2), f( – 3, – 5), and f(0,9). f(2,-5)=…

A: Given query is to find the value of the function at indicated points

Q: Determine an equation of the normal line (a line that is perpendicular to the tangent line) to the…

A: Let's find equation of normal line.

Q: Evaluate the improper integral or state that it diverges. P -dx Select the correct choice below and…

A: The given integral is: I=∫2∞32x2dx   As we know the Power Rule: ∫xndx=xn+1n+1+C ; n≠-1 And…

Q: The rate of change of revenue (in dollars per calculator) from the sale of x calculators is R'(x) =…

A: Here, R'(x)=(x+2)ln(x+2)

Q: Find the volume generated if the area between y = coshx and x- axis from x = 0 to x = 1 is resolved…

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Q: Determine whether the improper integral converges or diverges, and find the value if it converges.…

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Q: Evaluate the limit: lim (x - Inx)* x→0+

A: Using limit definition

Q: So x² (a²-x²) ³¹/2² dx

A: A detailed solution is given below.

Q: Evaluate the limit using the L'Hopital's Rule. 1 - cosh x lim x→0+ ln(x² + 1)

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Q: Evaluate the following definite integrals using the Fundamental Theorem of Calculus:

A: The given two integrals are:a∫-552xx2+2dxb∫01x3+1x+1dxFundamental Theorem of Calculus says:If Fx is…

Q: Which of the following expressions gives the length of the curve defined by R(t) = tij +In tk…

A: We have to find arc length expression for the given vector function.

Q: y-coordinate of the centroid of the plane region bounded by 17 What is the the x-axis and the…

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Q: The position of the sun at sunset, north or south of due west, depends on the latitude and the day…

A: We need to solve sinusoidal problem.

Q: Find y'. Show the step-by-step solution. Simplify your answer. 2x 1. y = In 4x²-1 2. y = log(tan x³)…

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Q: 1. (2x6x5 +7x³-3x² - 11) dx 2. f(9y2 +6y-4-y-5+1) dy (12x-x+x) dx 3.

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Q: What is the volume in cubic units of the solid formed when the region bounded by y = 3x - x^3,…

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Q: Volume of Solid of Revolution Problem Revolve about the (a) x-axis and (b) y-axis the area enclosed…

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Q: (a) a) ₁₁ (x² +y) dy dx. Show all your work! 2 (b) ***1 1 dy dx. Show all your work! 0 2 ¹y² ff 1 dx…

A: SOLUTION-

Q: Find the point(s) on the hyperbola x^2 - y^2 = 2 closest to the point (0, 1).

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Q: 5 sine cose de Sin²+ 3sine - 4

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Q: Let f(x) = e2sinx 1. Use the local linear approximation of fat x = 0 to approximate e2sin (0.01)

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Q: Let f(x, y) = (x³ − x)(y² – 1). Find fry(x, y).

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Q: 3 2 พ 2 cos2 4x dx

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Q: I. Evaluate the following limits 2. lim (3 + x)² x → +∞0

A: Given problem :- limx→+∞3x+x1x

Q: Sketch the graph of y = x-2 (x+3)²

A: The horizontal asymptotes by comparing the degrees of the numerator and denominator. Vertical…

Q: Prove that the last two digits of 2" cannot be 02 and the last three digits cannot be 108.

A: Note: As per our company guidelines we are supposed to answer the first question only. Kindly ask…

Q: Stan 3x sec 3x dx 3.

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Q: TU Evaluate a sec²20d0 8 a. 00.33 b. 0.5 c. 0.67 d. 0.25 e. NONE OF THE ABOVE

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Q: Determine the following integrals: 1.1.1 ļ (cos2x+sin x) dx x+1 .1.2 1₁ JF dx x + 2x+1 2 1.1.3 | ₁…

A: ∫ sin(ax) dx =-cos(ax)a+C       and     ∫cos(ax) dx =sin(ax)a+C ∫xn dx = xn+1n+1+C Note : As per our…

Q: Find fx(x,y,z), fy(x,y,z), f₂(x,y,z), and fyx (x,y,z) for the following. 3 f(x,y,z) = 4x³ + 2xy -…

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Q: 6. A family wants to build a fence in their backyard for their dogs, Charlie and Linus. The enclosed…

A: Let x and y be the dimensions of the rectangular field. According to given , Area(A)= xy= 4000…

Q: Evaluate the following integrals S- 3 • │e* − e| + (e* + = e) + e) dx e 0

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Q: 3 4-3x S²³ So dx dy

A: To evaluate the given double integral.∫03∫04-3x dx dy

Q: 4. y = √esinx + 2 5. y = 4x In 4x 6. xe = sin 5x - sin 3y

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Q: Find the volume of the solid generated by revolving the region bounded by the lines and curves y =…

A: Here we have to find the volume.

Q: Use implicit differentiation to find ∂z/∂x when xz+z2=yxz+z2=y

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Q: Evaluate the limits using the L'Hopital's Rule. lim (tan x) (sin x-1) x+2+

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Q: A ship leaves port travelling North West at 12 knots. A second ship leaves the same port 3 hours…

A: Given: Let first ship be Ship A and second ship be Ship B. Speed of ship A = 12 knots =12 nautical…

Q: What is the second derivative of y = 6x² 3x³ + x² - 5 ? - Oy"= 72x² 18x + 2 Cinema) Oy" 24x³9x² + 2x…

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Q: Perform the integration. π ¹3 sec³ x tan x dx √2 + secx 0

A: A detailed solution is given below.

Q: Find the value of t 20 + 10t - 4.905€ ² =0

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Q: 2. Find the interval of convergence of the power series & 3x गय

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Q: A particle is moving along a horizontal line such that its velocity in m/s is given by v(t) = 2t²…

A: A particle is moving along a horizontal line such that its velocity in m/s is given by vt=2t2-16t+30…

Q: What is the volume in cubic units of the solid formed when the region bounded by y = x^2 and y = 2x…

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Q: -2 Given f(x) = ²√4 - t² dt, evaluate the following. -2 (i) f (-1) (ii) f(0), by interpreting f (0)…

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Q: What is the center of gravity of the solid formed when the plane region bounded by y = x^2 and y=x+2…

A: We need to find center of gravity.