Write and evaluate the definite integral that represents the volume of the solid formed by revolving the region about the y-axis. y = V 25 - x2 4 y 3 2- 4. 5

Q: dx + 6x = 3yæ y- dy 1 1 x = (x – a²C)³ (y – y²C)³ Option 1 Option 2 1 1 y = (x + x²C)³ x = (y + y²C)...

A:

Q: cos(x + y), when x = 0,y = dx

A: Follow the procedure given below.

Q: Work of 3 Joules is done in stretching a spring from its natural length to 14 cm beyond its natural ...

A: Let's find. 

Q: Let f(x) = 7x- 13x-6, x2 1.5. Find the value of df 1 at the point x 234 = f(4). dx The value of dx (...

A: Given query is to find the the value of inverse function.

Q: For a particular commodity, the demand function is q=1/4 (400-p^3). a. find e when p=1. e=________ i...

A:

Q: Lesson 14 A. Find the derivative by implicit differentiation. Show your solution. 1. 2x 2y +5 2. x2 ...

A: Topic = Derivative As per guidelines , At  a time only one question with three sub-parts can be answ...

Q: Given z=. Find z z„= -2x , = 2x*3 Option 1 Option 2 z„- -2x Option 3 none of the above

A:

Q: Is the series convergent or divergent? Justify the answer

A: Follow the procedure given below.

Q: Solve the ff first order DE using integration method, by inspection, or bernoulli's equation

A:

Q: dx + 6x y- dy 1 y = (x – a²C)³ (y – y²C)³ Option 1 Option 2 1 1 (y+ y²C)³ (x + x²C)³ Option 3 Option...

A:

Q: 4. t(x) = (x - 3)3 5. h(x) = -x² 6. f(x) = V=x 7. f(x) = 2x2 %3D

A:

Q: (2v² + 4u²v)du + (4uv + 3u³)dv = 0

A: This question is related to differential equation.

Q: Given: g(x) = the square root of x, find g(x+h) - g(x) / h

A: This question can be solved by applying the concept of function and rationalization.

Q: Find the general term of the sequence, starting with n = 1. Determine whether the sequence converges...

A: Solution is written in below steps.

Q: Find the volume of the tetrahedron shown using the order dz dx dy. The tetrahedron is bounded by the...

A: Explained below

Q: QUESTION 5 For the following function, find the value of (a) f(-3) and (b) f(5), if possible. x²- 3 ...

A:

Q: 13 A small funnel in the shape of a cone is being emptied of fluid at the rate of 15 cubic centimet...

A: Let's find. 

Q: Use the Ratio Test to determine the convergence or divergence of the series. If the Ratio Test is in...

A: The series is given by ∑n=1∞8n! To evaluate: The convergence of the series using the Ratio Test.

Q: 3x-4 if-3 SXS4 If f(x) = find: (a) f(0), (b) f(1), (c) f(4), and (d) f(5). x -4 if 4<xs 5

A:

Q: 2. (s-s?-t)ds + (t + s² +t ²)dt = 0

A:

Q: In2 In 3 In3 In2 ! ! 'dpdv = | J 4. Show that e' p+v dvdp.

A: To prove that the integral

Q: SVa Inx dx

A: ∫xlnx dxBy using integration by parts=lnx∫x dx - ∫ddxlnx∫x dx

Q: Convert the Cartesian coordinate (– 5, 2) to polar coordinates, – 27 0. No decimal entries and answ...

A: The given point -5,2

Q: dy cos(x +y), when x = 0,y == dx

A:

Q: 6 36 36-y Top: y +z 36 Here is the region of integration of the integral dz dy dx. Rewrite the integ...

A:

Q: 1 dy 3 yz-+ y7 = 1, when x = 0, y = 3 dx

A:

Q: Solve the following differential equation:  xdx+ydy=(x2+y2)dx (2x2+y)dx+(x2y-x)dy=0 (xy2+x2)dy+ydx=...

A: As per the guidelines, we are supposed to answer only one question at once. Kindly repost the remain...

Q: The force on a particle is described by 2x 1 at a point x along the x-axis. Find the work done in mo...

A: topic- definite integral

Q: A small funnel in the shape of a cone is being emptied of fluid at the rate of 13 cubic centimeters ...

A: topic - application of derivatives

Q: u* + v*)du – uv*dv = 0 1 1 -5 и O Option 1 Option 2 1 1 u5

A:

Q: A roasted turkey is taken from an oven when its temperature has reached 183° Fahrenheit and is place...

A:

Q: Consider the curve, y with parameter (, and function f in 3 dimensional Euclidean space with coordin...

A:

Q: The position of a particle moving along a coordinate line is s=sqrt19+6t​, with s in meters and t in...

A: Given; st=19+6t   As we know that; The Power law; ddxxn=nxn-1 The Chain rule; fgx'=f'gx·g'x

Q: 6. yi+ yž = 1, when x = 0, y = 4 dx

A:

Q: Given R(t) =4 cos ti +(1+ 3cost)j + 5sintk. Find T(t). T(t) = sin ti -sintj + costk T(e) = sin ti -s...

A: Given :- Vector R(t) = 4 cos(t)i +(1+3 cos(t)) j +5 sin(t) k To find:- Tangent Vector T(t) 

Q: Calculate the volume of a bounded solid. 2) z = 5 – a*y , 1z=1 Draw the region over which we integra...

A:

Q: (х — Зу + 3)dх + (3х + у + 9)dy %3D 0

A:

Q: (w - 3x +3)dw + ( 3w + x + 9)dx=0

A:

Q: Sketch the region enclosed by the given curves. x = 3y2, x = 4 + 2y2 y y 12 10 8 6 6 8 10 12 2 1 2 y...

A: The region is enclosed by the curves,x=3y2, x=4+2y2

Q: Find a formula for the general term a, of the sequence, assuming that the pattern of the first few t...

A:

Q: (2? + y? + 1) dæ – (æy+ y)dy= 0 - %3D x +1 (x + 1)? Option 1 Option 2 (x + 1)-3 (x + 1)-1 O Option 3...

A:

Q: A tank, shaped like a cone has height.10 meters and base radius 3 meters long. It is placed so that ...

A: We have to find work done  to pull out all water from tank.

Q: n cos“(n) 2+ n3 Determine if the series converges or diverges and choose the option that describes t...

A: Using Dirichlet test.  According to guidelines we solve only first question. 

Q: Convert the Cartesian coordinate (6, 1) to polar coordinates, 0 0. No decimal entries and answer ma...

A:

Q: 2. Use the function h(x) = : a. Use a calculator to graph h(x). Make sure you have a window that is ...

A: This is a problem of curve tracing. By using online available calculator we will plot the graph as m...

Q: = 1, when x = 0, y = 4 %3D %3D

A:

Q: JA large cube of ice melts such that it maintains its shape. The surface area is decreasing at the r...

A:

Q: 3. Use g(x)=e* (x-a) and g'(x) =-2e (x-a)(x-ax-1) to answer the questions. a) Find lim g(x) and lim ...

A: This question is based on Finding limits using L hospitals rule.

Q: 3. The parametric equations r(t) = cos(t – t³),y(t) = sin(t – t°), t € R describe the position of a ...

A: