d dx sinh(Vx)=

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

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Q: 14. For the series Σn=1 (-1)" 3n0.3+8 S4= Include 4 decimals in your answer. Now find a bound for…

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Q: Find the area bounded by y³ = x² and x-axis, from x = 0 to x = 8.

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Q: Find a particular solution of as =10csc² 2t determined by s= 2 when t == . dt

A: dsdt=10csc2(2t)  s(π/4)=2 ds=10csc2(2t)  take integration both side

Q: Given x = y³+2y — In(y + 1), find the arc length for 0 ≤ y ≤ 3 B

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Q: THE AREA BOUNDED BY THE PARABOLA y² + x - 2y = 1, THE X-AXIS, AND THE REVOLVES ABOUT THE LINE LINE…

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Q: Let P be the point with Cartesian coordinates (6,9), and C be the plane curve with parametric…

A: The parametric equation,x=t2-t and y=2t3-1123

Q: example of properties of definite integral

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Q: r 1 1 sing at Ø 元-6

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Q: The circle of radius 1 centered at (-3, 4,1) and lying in a plane parallel to the yz-axis is a)…

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Q: y = (x² + 2)(x-3)

A: The objective is to find the derivative.

Q: S St. Not e (cos48)² 45 ds

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Q: Let The coefficient of x³ in the Maclaurin series for f(z) is: Answer: . You may explain your answer…

A: The given function is f(x)=9e2x-x A Maclaurin series is given by:-

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

A: Use the relation between cartesian coordinates and polar coordinates

Q: 5. Find the limit, if it exists. If the limit does not exist, explain why. sin x - COS X (a) lim x/4…

A: We have to find the limit of the following function.

Q: In the quadratic equation Ax2+BX+C =0, describe the roots when B2-4AC is positive. The roots are…

A: The given quadratic equation is Ax2+Bx+C=0

Q: 3 [² [v³ – y³]³ª a Jo ² dy

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Q: The paraterized curve below is rotated abour the x-axis. Find the area of the surface. x = cos³ (0)…

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Q: Calculate the effective interest rate for each of the following nominal interest rates: a. 3.25%…

A: This question can be solved using the concept of effective interest rate.

Q: One side of an open field is bounded by a straight river. Determine how to put a fence around the…

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Q: 2x³ - 4x² − x − 3 dx x² - 2x - 3 zln |x+1| +31n|x - 3| + C Option 1 2 In x + 1-3 ln|x - 3| + C…

A: Given, ∫2x3-4x2-x-3x2-2x-3dx

Q: Find the volume generated by revolving the area bounded by x² - 4x - 4y + 4 = 0 and y = 1 about the…

A: To find the volume generated by revolving the area bounded by x2-4x-4y+4=0, and y=1, about the line…

Q: If z is a function of x and y implicitly defined by əz əz find and əx ду at (x, y, z) = (0, 2, -1).…

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Q: 6. If y = 3√x, then what is y'? 2 A. y' == x 3 B. y' = 2/2 x3 C. y' = 1/ x3 D. y' = ¹/2 x 3

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Q: Find the arclength of the curve x = - with 3 ≤ t ≤ 4.

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Q: 2) Let f be continuous on [a, b], differentiable on (a, b) and positive (i.e., > 0) for all x ≤ (a,…

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Q: Find the transition points. y = 4x7 - 56x6 (Use symbolic notation and fractions where needed. Give…

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Q: x² 1) Let f(x) (Figure 24). Verify the X 1 following: (a) f(0) is a local max and f(2) a local min.…

A: Since you have posted a question having multiple subpart part as per guidelines we can solve only…

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

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Q: Find the slope of the tangent line to the graphof the polar equation 1 TU r = at Ø 1-sino 6

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Q: Ashley heard that he could triple his money in 12 years if he invested it in a large…

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

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Q: A bucket that has a mass of 25 kg when filled with sand needs to be lifted to the top of a 20 meter…

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

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Q: Consider the vector-valued function R(t) 1. Find the domain of R. 2. Show that R is continuous at t…

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Q: 2x - 3 Examine the function f(x):= x²+4 from the point of view of monotonicity and give its local…

A: This question can be solved using the concept of monotonicity and local extrema.

Q: A ball is thrown upward from the top of an 800 foot tower. It's height above ground, h, t seconds…

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Q: The population of a city is modeled by the equation P(t) = 357,512e0.25(t) where t is measured in…

A: We have to find how many years will it take for the population to reach one million.

Q: Find the area that are bounded by: y=x²+5x and y=3-x² from x=-2 to x=0.

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Q: (a) f'(x) = -12 X = 0,-1 (b) f'(x) = 0 X = 1,-6 (c) f'(x) = 12 x = 252 X X X

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Q: Find the indicated power using De Moivre's Theorem. (Express your fully simplified answer in the…

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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: Consider vector v = (1,2,2), point A(2,5,4) and point B(-1,5,1) - In center-radius form, find an…

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

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Q: Find the area bounded by the parabolas (x - 2)² - 9py = 0 and y² = 9p(x - 2).

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Q: [₂7-4x dx -2 Determine the value of [4f(x) dx given that [ƒ(x) dx = 10 and ſº ƒ (x) dx = 3. 27 sin…

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Q: Solve ²₂(x + 1)(x + 2)²(x² − 1)dx with and without the even-odd theorems (show both solutions).

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Q: A projectile is fired vertically upward with an initial velocity of 210 m/sec from a point 2 m above…

A: topic- algebra