"alse 1. The absolute extrema for a function f(x) will occur wherever f'(x) = 0 2. The rectangle with the smallest perimeter for a given area will always be a square.

Q: A rectangular plot of land is to be fenced in using two kinds of fencing. Two opposite sides will…

A: A rectangular plot of land is to fenced in using two kinds of fencing. Two opposite sides will use…

Q: 5. Does the function f(x) = If yes, what are they? If no, explain your reasoning. have absolute…

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Q: Evaluate the line integral [39a²³yzds with respect to s along the 2 curve C: x = t, y t, y = t²,₁…

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Q: 10. Find the area of the paraboloid x² + y + z² = 2 by the plane y = 0. (Hint: Implicit Surface)

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Q: Find sin 2x, cos 2x, and tan 2x if sin x= sin 2x = cos 2x = = tan 2x 010 X 1 and x terminates in…

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Q: ² fx ds, where C is с t a. the straight line segment x = t. y = from (0,0) to (16,4) b. the…

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Q: Find the indefinite integral. (Use C for the constant of integration.) 1₁ sin4 20 de

A: let  2θ=t⇒2dθ=dtThen∫sin42θdθ=∫sin4t dt2=12∫sin4t…

Q: Find Vf if f = 2 2 2 x² + y² + z² V.

A: Given,            f=1x2+y2+z2To find : ∇f

Q: Find the arc length L of the graph of r(t). L r(t) = 12 cos(t)i + 12 sin(t)j + tk, 0≤t≤ 2m

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Q: Find the sum of the series, if it converges. Otherwise, enter DNE. 6 Σ n(n + 2)

A: Given problem:-

Q: The heights on the graph of f'(x) correspond to the slopes of the lines tangent to the graph of f.…

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Q: Find T(t) and N(t) at the given point. r(t) = 6 cos(t)i + 6 sin(t)j + tk; t = T() 6 37 0, √/3 X N…

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Q: Find the total mass of the wire with density p whose shape is modeled by r. r(t) = t²i + 2tj + tk,…

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Q: 9. Which of the following is equal to feedt? A. ee C. eºx + C B. ee + C D. eºt + C 10. What should…

A: As we know that; The Power rule: ∫xndx=xn+1n+1+C And ∫c·fxdx=c·∫fxdx , where c is constant   (9).…

Q: Find the limit. lim 1-4(t i-8j+t² k)

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Q: Use Green's Theorem to evaluate the integral. Assume that the curve C'is oriented counterclockwise.…

A: This is a problem related to vector calculus. Based on the general formula of green's theorem we…

Q: Find the centroid of the region. NOTE: Enter the exact answers. (x, y) (?, ?) = y y=x8 1 8

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Q: A plane flying horizontally at an altitude of 3.4 miles and at a speed of 790 mi/hr passes directly…

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Q: Calculate[ri(t) r2(t)] and [r₁(t) × r2(t)] first by differentiating dt the product directly and then…

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Q: 5. Consider the surface obtained by rotating the graph of f(x) = 1/2, 221, around the z-axis. This…

A: We will show this using integration ∫1∞1xdx = ln x1∞ = limx→∞ln x = ∞

Q: Determine the volume of the solid obtained by rotating the region bounded by x=(y−2)^2, the x-axis…

A: Given:        x=y-22 The volume of the solid obtained by rotating the region about the x-axis is…

Q: Find the derivative of y = log2 4x Ox/In4 O 1/xln4 O4/1n4 @ 4/xin4

A: To solve the following problem

Q: Use the given derivative to find all critical points off, and at each critical point determine…

A: Follow the procedure given below.

Q: EXCERSICE X₁,, Xn Find i.i.d. E Uniform(0 X(1) + X(2) X(n)

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Q: Find the exact area under the graph of f(x) = = and x = 2. Area = 1 x+1 between r=0

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Q: Describe the graph of the equation. r = (8-2) 1+ 14tj It is a line in 2-space through the point…

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Q: 2) Use the graph of f to estimate the following limits. No work needs to be shown for this…

A: To evaluate the limits with the graph.

Q: 3. Sketch the graph of y=-2 sin Show evidence of transformations. Clearly plot your points. y=-2 sin…

A: Given:       y=-2sin2θ-π3+4  This is in the form of y=asinbθ-c+d       Here a=-2                b=2…

Q: f(x) = e²x cos(x) e2

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Q: Use differentials to estimate the relative error in the lateral surface area of a right circular…

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Q: Use differentials to estimate the amount of paint needed to apply a coat of paint 0.05 cm thick to a…

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Q: Select the choice that makes each statement true. x²+x-6 X-2 [Select] x +3 x²+x-6 lim X-2 X-2…

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Q: The Bernoulli's form of the differential equation x³ydx +(3x² − y³ )dy = 0 is

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Q: Find f '(x), if f (x) = e−5x 5e O-5e^-5x 5e^-5x 5x

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Q: dx 6x + x² V

A: To integrate by using the trigonometric substitution.

Q: Determine whether the sequence converges or diverges. If it converges, find the limit. If it…

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Q: dy (x + 1) dx = 1 x = 0; y=2

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Q: Solve the differential equation with complete solution.

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Q: Let f(x) = 3x5 - 5x³.

A: As per our guideline we are supposed to be answer only first three subpart of the question you can…

Q: Determine the volume of the solid obtained by rotating the region bounded by x=(y-2)^2, the x-axis…

A: Solution is given below:

Q: 4. f cot³ 2x csc¹ 2x dx = f cot² 2x csc4 2x cot 2x dx = f(csc² 2x - 1) csc* 2x cot 2x dx Let u =…

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Q: Non-Exact H.W: (2xy ey+2xy³+y)dx + (x²y^ey-x'y-3x)dy=0

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Q: Find the area between y = 8 sin x and y = 10 cos x over the interval [0, π]. Sketch the curves if…

A: We have to find out the area bounded by the two given curves.

Q: 2.S x² -4 X -dx

A: Note: Asper company guidelines, we are supposed to answer the first question only. Kindly ask the…

Q: X √2x²-4x-7 dx

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Q: Problem # 15 7 tan (2x) dx use: tan²x = sec² x - 1

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Q: 6. Which of the following is a particular solution to the differential equation when x = e5 and y =…

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Q: Question 20 Find the derivative of y = log₂ (x - 2)³ 1/(In2)(x-2) 3/(In2)(x-2) 2/(In3)(x-2)…

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Q: Confirm that the force field F(x, y) = yeyi+ xey j is conservative in some open connected region…

A: We have to find the work.

Q: Find for x³+y³ = 2. -4x O O (E) None of these ○ 3x² + 3y² = 0 2x *(*_*) O

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