Estimate the area under the graph of f(x) = √√x + 1 over the interval [-1, 1] using eight approximating rectangles and midpoints. Mn =

Q: A tank in the shape of an inverted right circular cone is full of water. The water weighs 62.4…

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Q: Evaluate the integral. -π/2 (cos(x) Jo Jo y sin(x) dy dx

A: let  D=∫0π2∫0cosxysin(x)dydy

Q: What are the spherical coordinates of the point whose rectangular coordinates are (4, 5, -3)? P 0 ||…

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Q: 6. x3 dy dx +3x²y = x

A: x3(dy/dx)+3x2y=x  We have to find general solution

Q: Identify the field below as conservative or not conservative. F = (9z+9y)i + (5z)j + (5y + 9x)k

A: The given vector field is:F=9z+9yi+5zj+5y+9xk

Q: 3. Let f(x) = x¹/3 and g(x) = 2x² + 5x – 1. A. Write out the equations for all four functions: ƒ(x),…

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Q: 2-x Find the domain of f(x) = 7+12x-13

A: The domain of the rational function is all the values except where the denominator is zero.

Q: Consider the following series. Evaluate the following. [ 0 / / Use the Integral Test to determine…

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Q: Consider the function f(x) = - +4. In this problem you will calculate √(- ³²3² + +4) dx by using the…

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Q: Find dy dx by implicit differentiation. x5-5xy = 29

A: We can solve the given problem by using the implicit differentiation method

Q: For each of the described curves, decide if the curve would be more easily given by a polar equation…

A: a) pass through point 0,0slope =  tanπ6 = 3b) pass through point 3,3slope = infinie (vertical line)

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

A: We need to perform differentiation.

Q: Evaluate 16 (²) ds, where S is the portion of cylinder x = y² that lies in the first octant between…

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Q: Determine whether the improper integral diverges or converges. 35 (¹350 dx O converges Ⓒ diverges…

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Q: A particle is moving with the given data. Find the position of the particle, s(t). = 5 cos(t) 4…

A: given,  a(t)=5cos(t)-4sin(t)given conditions,  s(0)=0 and v(0)=8formula of integration→(i)…

Q: IJ 18 17 16 15 14 13 12 11 10 9 8 7 6 5 4 3 2 1 2 3 4 Left endpoint Riemann sum for y = 2* on [0, 3]

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Q: Estimate the area under the graph of f(x) = x² + 2x from x = 1 to x = 5 using 4 approximating…

A: We need to determine the area f(x)=x2+2x from x=1 to x=5 using 4 rectangles and left end points.

Q: Use the arc length formula to find the arc length along the curve y=√100-x²,0≤x≤5.

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Q: Find the general solution. y"" - y" - 6y' + 6y = 0

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Q: Find all points (x, y) where f(x, y) has a possible relative maximum or minimum. Then, use the test…

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Q: Suppose that at t = 4 the position of a particle is s(4) = 8 m and its velocity is v(4) = 3 m/s. (a)…

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Q: 1. Find the following for the function f(x, y) = 3x³y² - 5x + 26y - 9.

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Q: The equation y= 2e65 is a particular solution to which of the following differential equations? B D…

A: An equation,

Q: Consider the function f(x) = 4 − |x| defined on [−4,4]. (a) Compute the left Riemann sum L12. L12 =…

A: We have to find the value of left Reimann sum and right Reimann sum and compute the area under the…

Q: Find the indefinite integral. (Use C for the constant of integration.) -3 (+²+3)³/2 dx

A: We have to integrate expression  -3/(x2+3)3/2 with respect to x

Q: Use substitution to find the indefinite integral. S9(9x - 8) dx [9(9x-8) dx =

A: let M=∫9(9x-8)6dx  formula of integration→(i) ∫xndx=xn+1n+1+c

Q: Evaluate the integral ² I = (1 + 4y - y²) dy.

A: Recall the formula: ∫1dy=y+C∫yndy=yn+1n+1+C

Q: 2 2. Evaluate: [x(x² − 1)² dx 1

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Q: Find the volume of the pyramid with base in the plane z = −7 and sides formed by the three planes y…

A: Here we have to use the concept of triple integration

Q: Two systems of equations are given below. For each system, choose the best description of its…

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Q: Find the angle 8 between the vectors in radians and in degrees. 5 [cos(3)i + sin(37)] 4 (²7)₁] u = 5…

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Q: V. Suppose f is a continuous function whose derivative f' has the following graph: -2 -1 3 2 Write…

A: Suppose f is a continuous function whose derivative f' has the following graph. To write TRUE if…

Q: Find the first 10 partial sums of the series. (Round your answers to 4 6 2 3 لیا 5 1 C Ë n = 1 Sn…

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Q: The Intermediate Value Theorem guarantees the existence of at least one real zero of the polynomial…

A: The Intermediate Value Theorem (IVT) is a fundamental theorem in calculus that relates to the…

Q: Find f. f(x) = f'(x) = √(3 + 10x), f(1) = 11

A: Given: f'(x)=x(3+10x)f(1)=11 We are required to find: f(x)

Q: Evaluate the integral using the indicated trigonometric substitution. S dx, 6x³ √x²+36 X = 6 tan(0)

A: The integral is ∫6x3x2+36dx   ; x=6 tanθ

Q: Two airplanes are flying in the air at the same height. Airplane A is flying east at 200 mph and…

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Q: The graph of f is shown below. (Click on a graph to enlarge it.) Evaluate the following integrals by…

A: Given graph,

Q: Find the volume of the solid generated by revolving the regions bounded by the lines and curves y =…

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Q: A 140-lb man carries a 25-lb can of paint up a helical staircase that encircles a silo with radius…

A: Given data for the question is÷

Q: Solve the initial value problem: f(x) = 6 cos x + 2 x, F(π) = = 2 + π²2²

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Q: choose for u. -) dx, so it is helpful to look for some expression in 1 9x + 4 dx

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Q: Find the volume of solid that lies within the sphere x2+y2+y2 = 4, above the xy-plane, and below the…

A: We need to use the spherical coordinates to find the solution of this problem Using the following…

Q: Find a set of parametric equations for the rectangular equation that satisfies the given condition.…

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Q: Suppose that a particle following the path c(t) = (t², t³ – 5t,0) flies off on a tangent at to = 7.…

A: We have to find the position of particle at time t1=9.

Q: Use the shell method to write and evaluate the definite integral that represents the volume of the…

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Q: Find the derivative of the function. M(x) = (2x²-3)/x 3

A: given  f(x)=(2x2-3)(x2-3x)we know→⇒ d dx(xn)=nxn-1⇒d dx(constant)=0

Q: Suppose an airline policy states that all baggage must be box-shaped with a sum of length, width,…

A: Let's call the length of one edge of the square base "w". Then the other two dimensions (length and…

Q: 1. The plane 3x - 3y -z = 4 intersects the paraboloid z = 1² + y² in an ellipse. Use the method of…

A: Here we can find the points on the ellipse where the paraboloid intersects the plane by setting the…

Q: = α; Suppose that Σ = 5 and Compute the following sums. 120 (a) (ai + b₂) i=1 120 = 120 (b) Σ(-16a,…

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