If R is the region bounded by y = x* – 1 and y = -x² – 1, find the volume V(S) of the solid S generated by revolving R about the indicated line. a. x = -1 using vertical strip b. x = -1 using horizontal strip

Q: Find the solutions of the system of inequalities by graphing: x + y > –1; 2x + y < -3

A: Given that: x + y &gt; -1 ; 2x + y &lt;= -3  We find the solution of the system of inequalities by…

Q: Find the volumes of the solids generated by revolving the regions bounded by the graphs of the…

A: As per our company guidelines we are supposed to answer only three sub parts of a question.kindly…

Q: 1.lf f(x) and g(x) are continuous functions, then SIF(x) ·g(x)] dæ S f(x) dæ · ƒ g(x) dæ. 2.lf G(x)…

A:

Q: The following figure shows the graphs of y - f(x) and y = g(x). together with the indicated areas.…

A:

Q: (1 point) Given 12-49 dt 1+ cos2 (t) f(x): %3D At what value of x does the local max of f(x) occur?…

A:

Q: _13. What is § 2sinx cos x dx? cosx A. In2 +C В. C. +C +C D. In2 _14. Which of the following has…

A: We use the method of substitution to  solve the given differential equations

Q: Let f(x) = x In(1+x*). For all æ € [-1, 1], it is known that %3D +o0 In(1+x) = £ (-1)" -xn+1 n+1 n=0…

A: Given: Now, for 7th degree Maclaurin polynomial for f will be,        ln(1+x)=∑n=06(-1)nn+1xn+1. We…

Q: 1. Find all the remaining zeros of this polynomial function 2 = x' + x° + 7x´ + 9x – 18, 3 if one…

A: To find all the remaining zeros of this polynomial function.Px=x4+x3+7x2+9x-18, if one zero is 3i.

Q: is a p-series. 57 - - ... 17 27 37 47 Select one: O True O False

A:

Q: 13.Using integration by substitution in f'æ° (x® – 2)*dæ ,what is du? O A (26 – 2)³ dx (xº – 2)dr…

A: Since you have asked multiple questions, we will solve the first question for you. If you want any…

Q: 1. Find D„f at P: f(x,y) = sin(8x – 5y); P (5,8)); u=((i)

A:

Q: 2. Let f(x, y) = (2x – y,x – 2y); (x, y) E R × R, (R is set of real numbers.) a) Show that fis one…

A:

Q: r = - 10i + (1 – 1² )j + t k O It is a parabola in the plane z = – 10, with vertex at (1, 0, – 10),…

A: Find your answer below

Q: 2" is convergent. The series 2 n=1 h+1

A:

Q: (a) Suppose that f is differentiable, positive and decreasing on (a, b] and has no critical points.…

A: Given problem:-

Q: Find the volume of the solid formed by revolving the region bounded by y = x – x and the x-axis (0 <…

A:

Q: Find r'(t), r"(t), and r'(t) · r"(t). r(t) = (t2 + 9t)i - 4t²j (a) r'(t) (b) r"(t) (c) r'(t) · r"(t)

A:

Q: Consider the following. u = i +j+k v = 21 + j - k Find u x v. Determine if u x v is orthogonal to…

A: u=i+j+kv=2i+j-ku×v=ijk11121-1u×v=i(-1-1)-j(-1-2)+k(1-2)u×v=-i-3j-ku×v=-i-3j-k

Q: For each specified discontinuity, sketch the graph of a possible function f(x) that illustrates the…

A: This is a problem related to limit and continuity. Based on the given RHL and LHL we will plot the…

Q: Find r'(t), r"(t), and r'(t) · r"(t). r(t) = 8 cos(t)i + 5 sin(t)j (a) r'(t) (b) r"(t) (c) r'(t) ·…

A: Solve it.

Q: Set up and evaluate the integral for finding the area and moments about the x- and y-axes for the…

A:

Q: Find the arc length of the graph of the function over the indicated interval. (Round your answer to…

A:

Q: 2. In the differential equation 4(3x+ y-2)dx-(3x + ydy -0, we let the substitution dw=

A:

Q: (a) Find lim 0 arctan(3r)

A: Since you have posted multiple questions which are not interlinked i can do first question as per…

Q: Use the shell method to set up and evaluate the integral that gives the volume of the solid…

A: Let gy be continuous and nonnegative, then, the volume of the solid of revolution formed by…

Q: In the differential equation 4(3x+ y– 2)dx– (3x+ y)dy = 0, we let the substitution dw=

A:

Q: dr Let A be the area of a circle with radius r. If dt dA when r = 5. dt 5, find 50 Question Help:…

A:

Q: Let 22-4z+4 f(x) = I-1 Find the derivative using appropriate rules of differentiation.

A:

Q: Below is a sketch of the graph of J.

A: we say at x=a limit exist if the both right and left side limit exits and equal at x=a

Q: (Show your solution) Compute the inverse of the function f defined by f(x) V+ 2. Determine the…

A: We have to calculate inverse of a function  And the domain and range of the inverse function.

Q: Find the solutions of the system of inequalities by graphing: ¤ + y 2

A:

Q: Find the gradient of the function at the given point. f(x, y) = 4x + 2y2 + 6, Vf(4, 2) = eBook

A: A detailed solution is given below

Q: 1. (2x+ y)dx-3(2x+ y+4)dy =0

A: Let's find.

Q: If f(x) and g(x) are continuous functions, then s Ldx 4. Lf(x)dx Sø(x)dx° g(x) 5. Sdx = In]x| +C and…

A:

Q: The following figure shows the graphs of y = f(x) and y = g(x), together with %3D %3D the indicated…

A: Given problem:-

Q: Write a definite integral that represents the area of the region. (Do not evaluate the integral.) 2…

A:

Q: Find the volume of the solid that results when the region enclosed by the given curves is revolved…

A:

Q: y" + 5y + 3y = 0, y(0) = 1, y(0) = 0.

A: This is a problem of differential equation. Solution consist of complimentary function and…

Q: Revolution

A:

Q: Which of the following series is convergent? 00 (-1) 4. n=1 O None of them. 00 2(-1) 6. n=1 00 6. 11…

A:

Q: The integral represents the volume of a solid of revolution. 27 x³ dx (a) Identify the plane region…

A:

Q: Find the volume of the solid generated if the region bounded by the parabola y2 = 4px (p > 0) and…

A: Given

Q: g(t) = 4T - n, where n is a constant. Suppose we want to evaluate | 9(t) dt. O dt | Va dt + dt - 4 a…

A:

Q: Find a polar equation for the curve represented by xy = 4.

A:

Q: If y = a³ + e*, find y(4) when a = 0

A: Given: y=x3+ex   As we know that; The sum/difference rule: f±g'=f'±g' The Power law: ddxxn=nxn-1 And…

Q: Use cylindrical shells to find the volume of the solid generated when the region enclosed by the…

A:

Q: fy = e2" 2-3 , then find y" at x = 0 Enter your answer as a decimal

A:

Q: 3. y = Væ – 1, æ = 5 , y = 0 , revolved at y axis

A: To solve the following problem

Q: Let f be a continuous function. Show that 2022 f(x) dx. 2022 dx

A:

Q: Find the volume of the solid that results when the region enclosed by 2 x² and x 4 2y? is revolved…

A: