Find the area bounded by the curves x² + y = 6, y = x, y = -2 and x = -2.

Q: 1) Find |R'(t)|, Make sure to simplify your answer 2) Find the distance traveled by a particle…

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Q: A sector of a circle has a diameter of 8 feet and an angle of 7 radians. Find the area of the…

A: Let's find area of the sector.

Q: 16. Find the area of the region bounded by the given curve: r = 9eº on the interval ≤0 ≤ 2m.

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Q: 1. Determine the infinite (oo or -o) limit as follows: x² - 2 (a) lim x2-x² - 3x + 2 sin x 1 x+ cos…

A: Topic = Limits

Q: Using Simpson's method 2 x³dx for n=4 is equal to Blank 1 (use 2 decimal places with proper rounding…

A: The Simpson's 1/3 rule for integration is given by, ∫ab f(x)dx≈Δx3f(x0)+4f(x1)+2f(x2)+4f(x3)+2f(x4)+…

Q: Given: parametric curve H defined by r(t) = tan-¹t and y(t) = eªt, where t = R (a) Find the slope of…

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Q: Find the volume generated by revolving about the y-axis the area bounded by y2= x-2, y=x-4 Use shell…

A: Here we have to find the volume by using shell method.

Q: ly If cosh x = then sinh x = Select one: True False If f is continuous on a closed interval, then f…

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Q: x6 cos(x³) A) True B) False |dx=0

A: We have to check by even or odd function

Q: Determine the area of the region bounded by x = ³√/y-1 from y = 0 to y = 1.

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Q: Using the method mentioned in Item #7, find the volume of the solid generated by 3 revolving the R…

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Q: A B D 0 Consider the integral f sin ¹x dx. If we let u = sin ¹x and dv = dx, the integral can be…

A: We have to above question

Q: 1f S₁ (x+5) dx = Sº (x+5) dx = 14, then the value of b is equal to If A) None B 3 с 4 D -3 E 2

A: We have to find the value of b.

Q: Consider the vector-valued function R(t) = (t³ — t, 2t²,2 — 21.²). 1. Find ||'(t) || (Simplify your…

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Q: 4 3. 2 1 -4 -3 -2 -1 2 -1- -2- -3+ 3. From the above graph of y = f(x), find the following limits:…

A: a)2  b) -2  c) -4

Q: Find the moment with respect to the y-axis of the area bounded by the parabola x = 9y - y² and y =…

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Q: Find Vector A and B such that A is parallel to , B is perpendicular to and A + B =

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Q: II. Solve the following problems: 1. A university holds an essay writing contest in English in which…

A: We have to find the winner essay.

Q: Determine if the function √x² + y² +1 x² + y² f(x, y): 1 2 is continuous at (x, y) = (0,0). If not,…

A: To find whether the given function is continuous or not at(0,0).

Q: Find the area of the region bounded by the curve y=x²-3x²-x+3 and x-axis from x=-1 to x=2. (Note:…

A: To find the area of the region bounded by the curve y=x3-3x2-x+3 and x‐axis from x=-1 to x=2.

Q: Q1: convert the Integral 1-X fydx to the polar coordinates.

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Q: Use Figure 1 to evaluate each trigonometric function of angle A. The side adjacent to angle A has…

A: As we know that; The trigonometric ratios;…

Q: 5 dx In evaluating 1 is same as evaluating lim (In(f(x))). Determine the value of f(x) if x=5.91.…

A: ∫ 351x2-9dx

Q: Write the complex number in polar form with argument between 0 and 2. 5/(1 + i)

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Q: Find the complete solution of e sinx- - Note: fe" du = e" + C dy cos² x=0. dx

A: e-y sin x-dydx cos2 x=0⇒dydx cos2 x=e-y sin x⇒ey dy=sin x cos2 x dx⇒ey dy=sin x cos x·1 cos x dx⇒ey…

Q: Given x - ³²+2y — In(y + 1), find the arc length for 0 ≤ y ≤4 8

A: The arc length of the curve x=f(y) for a≤y≤b is given by ∫ab1+dxdy2 dy

Q: S√4t² + 3 dt

A:

Q: Given: planes Π1 : 2x − 5y + z = −1 and Π2 : x + 5y + z = 5 intersecting on a line ℓ. (a) Compute…

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Q: Evaluate L L ³ xy² 1 3xy² dy dx.

A: SOLUTION-

Q: df Use integration to find f(1) when f(3) = 1000 and = 4(x+1)(x² + 2x)³. d x -24,272 -26,341 25,980…

A: Integrate on both sides of the given differential equation and find f(x) .

Q: Let z(t) = 5 cos(t) and y(t) = 3.sin(t) All answers should be decimals rounded to 2 decimal places.…

A: Given that,   xt=5.cost and yt=3.sint

Q: Given than han [ 1 (2) de = (z) dz=-4 and ® [1(e) de - [5 (2) de = 20 None of the given choices…

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Q: II. Consider the circle C1 : r = 1 and the roses C2 : r = cos 2θ and C3 : r = 2 cos 2θ, each of…

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Q: etan 4s | (cos (cos 4s)2 ds

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Q: 2-1 4s - 4 s² - 16/

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Q: For the cubic polynomial function f(x) = : ax³ + bx² + cx + d, find a, b, c, and d so that 0 is a…

A: Solution :fx=ax3+bx2+cx+d f0=2  givend=2   ... 1critical number :f'x=0f'x=3ax2+2bx+c3ax2+2bx+c=0c=0…

Q: • Find the sum of the following convergent series. lim lim lim tan ¹ (2n+ 1) - 346 11 11 11 [tan…

A: Given problem:-

Q: (b) f is concave down on (-∞, 1) and concave up on (1, ∞). (c) lim f(x) = -∞ and lim f(x) = ∞. x-1-…

A: As per the guidelines we can solve 3 parts only

Q: Calculate the integral, if it converges. If it diverges, enter diverges for your answer. 1 S₁749 dx…

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Q: dy Find the complete solution of 2e2¹ cosx- dx Note: [e"du=e" + C - sin² x = 0.

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Q: R(t) = (2 ln|sec t], sin 2t, cos 2t) Find the distance travelled by a particle along the curve…

A: Let's find distance traveled by a particle.

Q: Which of the following is not true? A √ in(x²) dx = lim_ sin(x²) dx 3 3 dx dx Ⓒ 1² B In(x²) - = lim…

A: Solution is done in step 2

Q: If you evaluate the integral expression |2x - 3|dx the result is Blank 1 (use fraction or decimal in…

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Q: Find the area of the surface generated when the given curve just sayin revolved about the x-axis.…

A: SOLUTION-

Q: A payment of $1,900 is due in 3 years, and $3,800 is due in 5 years. What single payment made today…

A: We want to find the amount he want to pay now

Q: 7 x = R¹, ƒ(x):=· + 3√x² 1-x 1+x² +ea² +1 +π².

A: see below the answer and calculation

Q: Show

A: Please refer to the image below

Q: Find the area bounded by the curves y-x² = -3,x+y = 3 and y = 0.5x.

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Q: Consider the points K(-1,0, 7) and M(1, -2,5), the vector MN = (1,4, -3), and the line with…

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Q: Using Trapezoidal method √x²dx for n=4 is equal to Blank 1 (use 2 decimal places with proper…

A: SOLUTION-