Set up the double (dydx) and triple (dzdxdy) iterated integral that will solve the volume of the solid bounded by z = 4 x², x+y = 4, x + y = 1 in the first octant.

Q: Find the volume generated by revolving the area bounded by x² + 4x + 4y + 8 = 0 and y=-2 about the…

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Q: Consider a right triangle with a side of length a opposite angle A. a side of length y opposite…

A: Given:  A triangle ABC right angled at C sinB=13

Q: 4. f(x) = 4x cosh 3x x² ; f'(2.7)

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Q: 7. Find the limit, if it exists. If the limit does not exist, explain why. sin (2x - 6) sin(4x12)…

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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: Calculate the integral approximations To and M6 for 10 x³ dx. Your answers must be accurate to 8…

A: ∫ab f(x) dx≈Tn=∆x2fx0+2fx1+2f(x2)+...+2f(xn-1)+f(xn) ∫ab f(x) dx ≈Mn=∆xfx¯1+fx¯2+...+f(x¯n) ; where…

Q: FIND THE VOLUME OF THE SOLID OBTAINED BY ROTATING THE REGION BOUNDED BY y = -10 + 6 x - x ², X = 1…

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Q: . The area bounded by the parabola y² + x - 2y = 1, the x-axis, and the line x = 2 revolves about…

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Q: A certain family in Sitio Calculus opened a t-shirt business last year. The family started with 50…

A: Given: fx=x2-2x+3 Since, the marginal cost function is the derivative of the total cost function,…

Q: 3) Use L'Hopital's Rule to evaluate and check your answers numerically: sin x (a) lim X x→0+

A: Solution: a) limx→0+sin xx1x2

Q: 4. Find the limit, if it exists. If the limit does not exist, explain why. 3x²+4-4 (a) lim x2x² - X…

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Q: vy B. Find the derivative of function f(x, y, z) = 3e* cosxy + ex² + Inzx at point P(1,0,) in 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: The rational expression A TRUE B FALSE 1 (9x² +16)² can still be decomposed.

A: this can not be decomposed. This statement is false.

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

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

Q: a.) Solve the equation z³ − 1 = 0 15 1 √3 b.) Evaluate (-+-+3) " 2 2

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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: Find the value of C so that the function is a density function. f(x) = [Cx¹ if 0≤x≤ 9 10 otherwise

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Q: a. Use the definition mtan = lim f(a+h)-f(a) h h→0 b. Determine an equation of the tangent line at…

A: As we know that; The slope of the tangent line to the curve is equal to the derivative of the…

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

A: Given: Now, we find the mentioned ratios. sin A=662+102=6234=334cos A=1062+102=534tan A=610=35

Q: Write z₁ and 2₂ in polar form. Z₁ = -40, Z₂ = √√3+1 Z1 = Z2 = Find the product z₁z2 and the…

A: The given complex numbers,   z1=-40, z2=3+i

Q: problem. Check that the following Function is harmonic and determine it it is a harmonic Conjugate.…

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Q: 39 9. A curve with polar equation r = 6sin0+13cose represents a line. This line has a Cartesian…

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Q: Find the area bounded by the curves y = x(x − 1)², y — axis, and the line y = 12.

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Q: II. Find the sum of the following convergent series. lim = = = lim lim 0-2 1 [tan ² (2n-1) - tan²¹…

A: Given problem:-

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

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Q: Find the exact maximum and minimum volumes (in cm) of a rectangular box whose surface area is 1,300…

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Q: Find the volume of the solid generated by the region bounded by y - x² = -3, x+y = 3 about y = -5.

A: The equation of the curves are given by C1: y-x2=-3 ⇒y = x2-3 C2: x+y=3 ⇒y=3-x To evaluate: The…

Q: A particle is moving along a line in such a way that v centimeters per second is the velocity of the…

A: Velocity of the particle is given by:vt=9sin 3πt

Q: Find the area bounded by the parabolas (x - 1)² = 4ay and y² + 4a = 4ax.

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

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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: 9. y(y² + 1)dx + x(y²-1)dy = 0 Ans: + xy = c

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Q: 5. (4xdy+3ydx) + x³y² (xdy + ydx) = 0 Ans: 6x³y² + x6y6 = c

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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

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Q: 4 2 dx : 5₂² In evaluating is same as evaluating lim cos-¹(f(x)). Determine the value of f(x) if…

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Q: 6. Find the limit, if it exists. If the limit does not exist, explain why. tan 5x sin 6x (a) lim x-0…

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

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

Q: Give the following infinite sum and limit: 8 2n-1 3n+2¹ n=4 a) rsin r (b) lim 20 x² + e²-1

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Q: Find the volume of the largest right circular cone that can be incribed in a sphere of radius 3. 3 y…

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Q: Find the area of the parallelogram with vertices P₁, P2, P3, P4 P₁ = (1,3,3), P₂ = (1,2,2), P3 =…

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Q: 7. Find the limit, if it exists. If the limit does not exist, explain why. - (a) lim sin (2x 6)…

A: solution is given below

Q: Q1: convert the the Integral - (x² + y²)dydx to

A: Use the relation between cartesian coordinates and polar coordinates

Q: For what value of the constants A and B is the function f continuous on (-∞, ∞)? A√x+6-1 for x 3

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Q: pair of parametr quations is given. x = e4t y = et (a) Sketch the curve represented by the…

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Q: Solve the first order linear ordinary differential equation x sin x dy dx + (sin x + x cos x) y =…

A: Here, the given DE can be written as: xsin xdydx+(sin x+x cos x)y=xex⇒dydx+sin x+x cos xxsin…

Q: Considering C is a curve which has the following parametric equations: 1 t³t+1, C = { x (t) = { 1³3…

A: Parametric equation

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: 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: Calculate the integral, if it converges. If it diverges, enter diverges for your answer. 1 S₁° 19 dx…

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