Given x = y²+2y 8 - In(y + 1), find the arc length for 0 ≤ y ≤ 2.

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: dy Find the complete solution of 2e-2 cosx-sin²x = 0. dx Note: [e"du=e" + C

A: The given differential equation is 2e-2y cos x-dydx sin2x=0⇒dydx sin2x=2e-2y cos x⇒dy2e-2y= cos x…

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

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Q: If S x²+x-2 (x2-1)(2x-x²) dx AS + Bf f(x) dx + D f g(x) dx, then x dx can be resolved into A ...

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Q: Evaluate L L ³ xy² 1 3xy² dy dx.

A: SOLUTION-

Q: In evaluating S₂²² 2 dx 2 XV x²-4 is same as evaluating lim cos-¹(f(x)). Determine the value of f(x)…

A: We have to find the value of f(x) at given x.

Q: By method of Integration by Partial Fractions, A B(2x-2) + C (x³+5x²+6)dx (x²–2x+5)² = √ [₁²-2² +…

A: According to our guidelines we are supposed to answer only the first question if you want any…

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

A: Applications of differentiation

Q: Question 1 Iff and g are continuous on [a,b] and f(x) ≥ g(x) for all x € [a,b], then [f(x)dxz g(x)dx…

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Q: Find the Area of the Surface obtained by rotating the curve about the x - axis y = cosh x, 0≤x≤1

A: Area  of surface is obtained.

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

A: As we know from the Simpson's Rule: ∫abfxdx=∆x3fx0+4fx1+2fx2+4fx3+2fx4+...+4fxn-3+2fxn-2+4fxn-1+fxn…

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

A: I have shaded the area green which is to be calculated

Q: What monthly compounding nominal interest rate is earned on an investment that doubles in 10 years?…

A: We have to find the interest rate.

Q: Let r(t) = t - sin(t) and y(t) = 1- cos(t) All answers should be decimals rounded to 2 decimal…

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Q: Find the area of the surface generated by revolving x=√(8y-y2) on the interval 2≤y≤5 about the…

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Q: This answer is incorrect do you know why?

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Q: 3x + 2y = 6; x = 0; y = 0; axis OY. Find the moment of inertia.

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Q: How long will it take for an investment to at least double its original amount if it is growing at…

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Q: Consider the function. x³ + 12 f(x) = X Determine the intervals on which f is increasing,…

A: A function f (x) is increasing on the interval I if f'(x) >0 for x in I. A function f (x) is…

Q: Consider the vector-valued function 4t-8 [{m(3. In(3-t), 5,31²-8 8 R(t) 4-1² (0, -1,4), 1. Find the…

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Q: 2r find the moment with respect to the wavic of the area hounded by the parabola v - Av-172 and v

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Q: (b) p = 2 sin p cos 0

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Q: z²√(-z² + 1)5 dz

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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 volume generated by revolving the area bounded by y² - 4y - 4x + 4 = 0 and x = 1 about the…

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Q: Solve f(x + 1)(x + 2)²(x² − 1)dx with and without the even-odd theorems (show both solutions).

A: Solved below.

Q: Find the area of the surface generated when the given curve is revolved about the given axis.…

A: We know that surface area generated when the given curve is revolved about the given axis…

Q: True or false Unlike the anglet in the trigonometric function cost, the t in the cosht represents an…

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Q: State the initial value theorem. Verify the theorem for the functions: (a) 3-4 sin t (b) (t-4)² and…

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Q: Given x = y²+2y 8 - In(y + 1), find the arc length for 0 ≤ y ≤ 3

A: Given: x=y2+2y8-ln(y+1) The arc length is: L=∫ab1+dxdy2dy Now, dxdy=dy2+2y8-ln(y+1)dy…

Q: Find the exact length of the polar curve described by: r = 2e-0 on the interval 7 6" π ≤ 0 ≤ 9π.

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

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Q: The population of a town is decreasing at a rate proportional to its size. In 1980, the population…

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Q: Which of the following is not true? 5 dx dx (A) lim S o 25-x² c+5-0 25-x² 3 dx dx So in (x²) B √₁…

A: We have to determine integration

Q: Given: vector-valued function R(t) whose derivative R'(t) = (4t, 6t, −12t) (a) If R(0) = (-1,4,-5),…

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Q: Use the method of cylindrical shells to find the volume generated by rotating the region bound by…

A: Volume of solid is evaluated using cylinderical shell method.

Q: Find the average value of f(x, y) = sin(x + y) over a. The rectangle 0≤x≤ 1,0 ≤ y ≤ n b. The…

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Q: 3- Air at 25°C and 100 kPa at a relative humidity of 75 percent. The parti pressure of water vapour…

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Q: True or false √2 If cosh x = V, then sinh x = 2. It is possible for a function to have an absolute…

A: To determine whether the following statements are True or False.1 If cosh x=62, then sinh x=22.2 It…

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

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Q: 9. ydx - 4xdy = y'dy; y(4) = 1 Ans: -y²=

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Q: 4. Find the limit, if it exists. If the limit does not exist, explain why. 3x²+4-4 (a) lim x2x²x2 2…

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Q: _ ²+2y — In(y + 1), find the arc length for 0 ≤ y ≤ 3 8 Given x =

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Q: = Find the area bounded by the curves -x + y² = 8, x = -2y and y

A: Follow the procedure given below.

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: The length of the hypotenuse is 11. a is the length of the side opposite the 10° angle and b is the…

A: Solution is here

Q: 2. Find the equation of the tangent lines and the normal lines to the curve y = 2x² +3 at the point…

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Q: 3 [² [v³ – y³]³ª a Jo ² dy

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Q: q4

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