b) Find the volume of the solid obtained by rotating the region bounded by the curve y = -x² + 11 and y = x² + 3 about the x- axis.

Q: If g = xy + yz + zx and Ē = x²yī+ y²zī+ z²x k, find F. grad g and cross product of F and grad g at…

A:

Q: i) Find the general term (an) of the sequence 3e-¹, 10e-2, 29e-³, 66e-4, 127e-5,218e-6, ... ii)…

A: The given sequence is;  3e-1, 10e-2, 29e-3, 66e-4, 127e-5, 218e-6, ...

Q: Q4. Let R be the annular region lying between the two circles x² + y² = = 1 and x² + y² = 16.…

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Q: Sketch the graph of the equation by point plotting. ( y = x + 2 10 0

A:

Q: Air traffic controllers continuously monitor the angles of elevation and to an airplane from the…

A: Concept: The angle of elevation: The angle of elevation is the angle created between the line of…

Q: Refer to the figure and find the volume generated by rotating the given region about the specified…

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Q: Solve the equation for 8, where 0 ≤ 0 ≤ 2π. (Enter your answers as a comma-separated list.) 2…

A:

Q: Consider the region B under the graph of y = 3x² + 1, x [1,3], and above the x-axis. Find the area A…

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Q: Determine whether the series +∞o 1 Σκος (7) - co ¹ ( ² ) - COS ¹ (2 + ₁)] \n n=1 converges or…

A: We have to find whether the series converges or diverges.

Q: Suppose we are asked to compute the 100th derivative of x 3 . How can we obtain the answer in a fast…

A: Solve the following

Q: Find the point on the parabola y= 22 that is the closest to the point (8,11/2) on the Cartesian…

A: answer is in next step. i am answering three subparts as per guideline.

Q: State the range of f(x): {y € Ry> 4 -3} {ye Ry - 4 3 {y € Ry#0} {y € Ry>0} } = 1 3x +4'

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Q: Use spherical coordinates to evaluate the mass of a solid given by the integral below: 2 To LT SVET…

A:

Q: If y=-2x² + sin x solve for the differential of dy.

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Q: Calculate the following line integrals in a counterclockwise direction around the triangular path as…

A: Let's solve given double integration.

Q: 5. Find the divergence and curl of the vector field F(x, y, z) = (xy - 2², 2x+cos(yz), 2y² - sinz)…

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Q: 2. f cos²xsin² xdx

A:

Q: When you wrote Note: and then gave that formula what is the name of that formula because I cant find…

A: Let's solve.

Q: (a) cos(8): = √2 2

A: answer is in next step. please give a like .

Q: Determine whether each of the following vector fields is path independent (conservative) or not. If…

A: Solution is given below:

Q: Let v = (2, -1, 5) and u = (5, -7,3). Find 37 - 5u

A: We have to find 3v - 5u

Q: Wallis Formula Evaluate the following integrals. sin (3x) cos5 (3x) dx 1. 2. 16 4 [*³* sin³(2x) dx

A: Note:- Since you have asked multiple question As per our policy, we will solve the first question…

Q: Prob. 5 (a) () Find all points where f is discontinuous. Classify these points (if any) as removable…

A:

Q: Calculate the future value of end-of-month payments of $6,000 made at 2.64% compounded quarterly for…

A: To find the amount after 5 years.

Q: Convert the point (√3, 1, 0) from Cartesian to spherical coordinates.

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Q: Q5. Evaluate the triple integral ²³ cos (y²) dz dx dy.

A:

Q: Find an equation for the surface obtained by rotating the line z = 7y about the z-axis.

A: On solving this we will get

Q: If f is an even function and fº, f(x) dx = 2 and f f(x) dx = 9, find ſº ƒ(x) dx. (Use symbolic…

A:

Q: A cable hangs between two poles that are 70-ft apart. The two poles are both 40 foot high. Sag is…

A: Let's solve length of cable.

Q: 7. Given f(x)=√x² + 3, determine p(x), q(x), and r(x) such that f(x) = p(q(r(x))). ✓✓

A: We need to find p(x),q(x),r(x)

Q: 1. S x² (x+1)4 - dx

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Q: Evaluate f x²-x-5 x(x²-x-2) dx

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Q: y" + 3y' + 2y = U₂(t); y(0) = 0, y'(0) = 1

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Q: i) Find the general term (an) of the sequence 3e-²,4e¯4,5e¯6,6e-8, 7e-10, 8e-¹2,... ii) Calculate…

A:

Q: 2 + y²

A:

Q: 4. Coffee at temperature 180°F is cooling in a room with constant temperature 75°F. If it takes for…

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Q: Enter the absolute amount and argument for the number 3/2 √ 2+ 3/2 √2 i.

A:

Q: 27. Write an equation for the piecewise function graphed below. H toolkits. -5 -4 -3 -2 -] 5- + to 2…

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Q: The cost function for a particular product is given by C(x)=0.001x^3 −0.24x^2 +27.9x +110 dollars,…

A:

Q: Given the same three points P (1, 4, 6), Q (-2, 5, -1)  and R (1,  -1, 1).  Find a vector equation…

A: We can find vector equation of the line segment from Q to R .

Q: Let r(t) = 21²i+tj+t²k. (a) Find the unit tangent vector T(t) and T(3). (b) Find the principal unit…

A: As per our guidelines we are supposed to answer only first 3 sub-parts. kindly repost others.…

Q: Determine the particular solution. (xy)dy – (3x² + y²)dx = 0; Y(1) = 1 O 3ln(x) + 12 = 1²² 2x² O…

A: Let's solve differential equation.

Q: V. Consider the power series +∞0 n=1 (x + 1)" +1 1. Determine whether the resulting series when x =…

A: We need to find convergence and radius of convergence.

Q: x5 + x4 (5x6 + 6x5)² J dx

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Q: Find the derivative of y = (2x³-6)*(3x-2)2

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Q: Divide. If the divisor contains 2 or more terms, use long division. 21x²-37x+12 7x-3 Divide. 5 9 4x…

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Q: (1) Use the definition to prove that if x₂ → 2 then (2x, +1)/x → 5/2.

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Q: So (2+7x) et ¹ dx

A:

Q: Find the exact value of the definite integral below, using the substitution u = x - 1²/1. X (√6+√2)…

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Q: Evaluate the following: 1. [cos 3xdx

A: We can solve the integration as below.