What is the surface area of the solid generated by revolving about the y-axis, y =1- a2, on the interval0

Q: 9. Oil spilling from a ruptured tanker spreads in a circle on the surface of the ocean. The area of…

A: Oil spreads in circle on surface of ocean. Area of circle is A=πr2.…

Q: Use Intermediate Value Theorem to explain why the function has a zero in the given interval. [0. 1]…

A: Given problem:- Use Intermediate Value Theorem to explain why the function has a zero in the given…

Q: .9

A:

Q: Find the nth Taylor polynomial for the function, centered at c. f(x) = In(x), n = 4, c = 6 P4(x) =…

A: Solution

Q: Pr. #3) Prove that the limit does not exist. cos(4ry)- 1 lim (x.v)-(0,0) 2r + 3y4

A:

Q: By considering different paths of approach, show that the function below has no limit as…

A:

Q: C Find the firet order parhal derivohve of fx,y,2). e W y-10y²23+ 43x hCs, t) =° t*In ts) + 32 4,5…

A: We want to find first order partial derivative of the given functions.

Q: Find all the derivatives of the following functions f (x) = x° + 4x* + 3x° – x² + 6 - 1. 1 12 g(x) =…

A: Let's find.

Q: What are the local extreme values of the function f(x) = x' – 3x + 2? a. None of these. O b. Local…

A:

Q: 19. cos (20) 1/2

A: We will find the value of θ in the following step.

Q: lim X- Sin X X3

A:

Q: Find a formula for the nth term of the sequence. - 1, 4, - 9, 16, -25, .. Determine the sequence's…

A:

Q: Apply your understanding of derivatives to determine any intervals of increase for the function…

A:

Q: b. dx Vr - 2x2 + 1

A: To evaluate: I=∫x5x4-2x2+13dx=12∫x22(x2)2-2x2+132xdx Substitute x2=u⇒2xdx=du

Q: Let B be the sphere x2 + y? + z? = 1. The volume of the portion of B contained in the first octant…

A: Given : B be the sphere x2+y2+z2=1

Q: The slope of a tangent line at (1, 4) is 2. What is the equation of the line? Select the correct…

A: As asked we can answer the question with out all explanation in the following steps

Q: dx J Vx² – 25

A:

Q: (iii) Extremum point(s), (iv) The interval of concavity, (v) Inflection point.

A:

Q: 5. w = x tan-y - 2=

A: Given: w=xtan-1y-2xyz

Q: 2r 2r If the total volume of the cylinder and square block is 30 cm', express h in terms of r.

A: Given that total volume Volume of cylinder+volume of cuboid=30 πr^2 ×h + 2r ×2r ×r =30 πr^2 × h…

Q: Let f(x) - 16. The arc length of the graph of f(x) over the interval [5, 9] is given by the definite…

A:

Q: what

A: We will find the velocity and time

Q: Find * L(e2t t²)

A: We will use first shifting Theorem to solve this question.

Q: Evaluate (f-1) '(2) for the function f (x) = /x³ + x² + x + 1.

A:

Q: What are intervals of concavity of the function f(x) = -2x – 6x² – 3 ? a. Concave upward on (-o, -1)…

A: Given query is to find the interval where function is concave up and down.

Q: Sketch the region of integration and evaluate the integral. 1 y || 15y5 e xy dx dy ... Sketch the…

A: To sketch the region of integration and then solve the given integral.

Q: 1. Evaluate the following integrals. 2" – 4" - dy - с. 2+ 49

A: To evaluate the given integral.∫2y-4y2+4y dy

Q: Find (x, y, z). (Let P = (7, 7, 0) and the Midpoint = (0, 5, 5).) (х, у, 2) %3 Midpoint (х, у, 2) P

A:

Q: The power series representation of 8. f (x) = x+7 centered at x=2 is: O :- 8 8 8 8 81 (*- 2) + (x-2)…

A: Topic = Series

Q: x² – 2x – 1 dx I ( – 1)²(x² + 1)

A:

Q: Find the linearization L(x,y) of the function f(x,y) = e 4* cos (y) at the points (0,0) and 0, The…

A:

Q: Given the vector ủ = (2,0,1) (a) Solve for the value of a so that ū and i = (a, 2, a) form a 60…

A:

Q: Plot the point that has the given polar coordinates.  2,  3π 4

A: We have to show the given point on the graph.

Q: Find * S L-1 (s²–4s+13.

A:

Q: Find the nth Maclaurin polynomial for the function. f(x) = sin(x), n = 6 Po(x) =

A: nth Maclaurin polynomial for the function f(x) :       Pn(x) = f(0)+f'(0)x +f''(0)…

Q: (a) Find the series' radius and interval of convergence. Find the values of x for which the series…

A:

Q: つX

A: Given:f(x,y)=tan-1xy

Q: 3. xy' =y-xe/x ANS y =-x

A: To find out the solution of the differential equation.

Q: 1. Find the total differential dw. x + y +z 3. w = xyz

A:

Q: 20. tan (20) = -1 %3D

A: We have to find the value of θ.

Q: Integrate using any applicable method. Be sure to give an exact answer. (3z+1) Enter your answer in…

A: Solve the following

Q: sin x ferentiate y = (x² + 1)°

A:

Q: 04: S+* + 1)sin z dz =

A:

Q: What are the two values of k closest to -7 for which , sin2 (x +7)- cos2(x +7) da has a value of 12…

A:

Q: Change the Cartesian integral into an equivalent polar integral. Then evaluate the polar integral. 3…

A:

Q: Q.NO. 1 A box contains cards numbered 6 to 50. A card is drawn at random from the box. The…

A:

Q: On what interval(s) is f(x) increasing? Decreasing? Explain

A: Given the graph of the f'(x)

Q: Find the linearization L(x,y) of the function at each point. f(x.y) = x² + y? + 1 а. (2,1) b. (0,2)…

A:

Q: Using Laplace transform to solve the IVP: y" – 9y = e *, y(0) = 0, /(0) = 0 %3D we find the solution…

A: The given IVP is y''-9y =e-3t,   y(0) =0, y'(0) =0 To solve the problem we must know the following…