2. For each problem, sketch the curves of the given equations in a graph and find the volume of the solid that results when the region enclosed by the curves is rotated about the given axis. (a) y = 2x + 2, and y = x² + 2; about line y = -1

Q: A 90 ft 120 ft 134.2 ft

A: In a public park, a triangular region of grass is bounded by walkways. Sprinkler heads are placed…

Q: Simplify 2 + √-27 . О 2+3iN3 2+9i√3 00 0 2-91√3 о 2-3i√3 O

A: 2+-27

Q: A. Calculate Jovit 1+ 3x2 - 4y ds where C is the curve x = t, y = t²/2, 0≤ t ≤ 2.

A: Since you have asked multiple questions in a single request so we will be answering only first…

Q: Find the coordinates of the point (x, y, z) on the plane z = 4x + 4y + 3 which is closest to the…

A:

Q: Multiply and write the answer in the form of a + bi. (-9) (2-√√-25) O 18+45 i O 6+15/ O 15+6i O -18…

A: (-1)1/2  = i  (25)1/2 = 5  (a.b)1/2 = (a)1/2(b)1/2

Q: If g(x) = 3x - 7 and h(x) = (fog)(x) = 9x² - 42x + 49, then f(x) Using g(x) and f(x), determine…

A: Given: g(x)=3x-7h(x)=(fog)(x)=9x2-42x+49 We are required to find: (gof)(x)

Q: Simplify. 2 [5x 5y2 0]

A: We need to simplify the given expression.

Q: Evaluate N εν Σ √19 lim N→∞ N 19 19 19(1) - 2

A: limN→∞1N∑j=1N19-19jN2

Q: -1 3. Use the IFT to prove dx √1-x² (HINT: you'll need to draw a triangle like you did in precalc,…

A: ddxarccosx=-11-x2

Q: The fourteenth value of a geometric progression (GP) is 45. Determine the first value of the GP. O…

A: We need to find the first term of geometric progression with the given data.

Q: 3. A box container, in a shape of a rectangular prisin, has a square base. 64000 inch³. (a) Find the…

A:

Q: esin x dx

A:

Q: Estimate the area under the graph of f(x) = 3 sin x ㅠ between x = 0 and x = using five approx- 2…

A: To estimate the area under the graph of fx=3 sin x between x=0 and  x=π2 by using five…

Q: -8x + 9x Let f(x) = x3 F(x) = Find F(x), where F(x) is the antiderivative of f(x) that passes…

A: fx=-8x6+9xx3 fx=-8x3+9x2 fx=-8x3+9x-2 F(x) is the antiderivative of the function f(x)  Fx=∫fx dx…

Q: 8. Evaluate the triple integral of xyz dz dy dx for the following limits: z from 0 to y, y from 0 o…

A:

Q: Evaluate the line integral [V. dr for the following function and oriented curve C (a) using a…

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Q: Use the Limit Comparison Test to determine the convergence or divergence of the series. lim 11-00 Ο…

A: The given series: ∑n=1∞1nn6+3We need to check the convergence of the series using the limit…

Q: Consider the equation . y=x^2 -6x+3 a. Find all critical points for the graph. b. Determine all…

A:

Q: For each function graphed below, state whether it is Graph 1 Graph 2 -8-6-4-2 - N -2 4 68 x

A: If a horizontal line intersects the graph of the function, more than one time, then the function is…

Q: Find the work done by the force field F in moving an object from P to Q. F(x, y) = (2x + y)i + xj;…

A: Fx,y=2x+yi+xj

Q: 4 x-0 2ex - 12 1 3 C. - 0.4 Find Lim- A. B. D.

A: Here we have expression where x is approaching to zero. Need to find the value of the expression…

Q: Simplify -2√-36. O -72i O -12/ O 72i O 12/

A: The expression is given by -2-36 To evaluate: The simplified form of the expression.

Q: What is the SUM of the first 10 terms for the following geometric series: 2- 6+18- 54+... A. 59048…

A:

Q: The figure below shows f.  If F′=f and F(0)=0, find F(b) for b=1, 2, 3, 4, 5, 6, and fill these…

A: The graph of f is  And, F'=fF0=0 It is known that, ∫abfdx=Fb-Fa ∫abfdx=Area under the graph of f…

Q: Use L'Hôpital's rule 1. lim x →+∞ sin -18 X 2 X

A:

Q: d) ftan 5x sec³x dx

A:

Q: The function f(x) = - 4x³ + 11.76x² + 90.792x + 6.31 is increasing on the open interval ( It is…

A: Given: The function fx=-4x3+11.76x2+90.792x+6.31 To find:   The open intervals on which the…

Q: Find the critical numbers of the function f(x) = - 12x³ - 75x¹ + 40x³ - 2 and classify them.

A:

Q: Use technology to perform the following steps for the sequence given. a. Calculate and then plot the…

A: The solution is shown in step-2

Q: If limx→.3[x³ + f(x)] = -29, use the Rules of Limits to evaluate limx→.3[36x^² + f(x)- 3x]. O a. 11…

A: limx→-3x3+fx=-29

Q: 3.4.1. Using Definition 3.35, prove that each of the following functions is uni- formly continuous…

A:

Q: Find the angle between the diagonal of a cube of side length 15 and the diagonal of one of its…

A: Let side length = a. Length of diagonal of cube on one of its faces = a√2 Length of diagonal of cube…

Q: 5 and 6 please

A:

Q: For each problem, sketch the curves of the given equations in a graph and find the area of the…

A: Given curves equations y=lnx,y=1-x,y=2

Q: Find the absolute maximum and minimum values of the function over the indicated interval, and…

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Q: Multiply and write the answer in the form of a + bi. (-4) (5-√√-9) O -6+10/ O 20+12/ O -10 +6/…

A:

Q: Perform the indicated operation and write the answer in the form of a +bi. (5+3)-7i O -7+81 O-2+3i O…

A:

Q: Use L'Hôpital's rule 1. lim x →+∞ sin 1 ~|8| 2 x

A:

Q: Use the given transformation to evaluate the integral. JJ² 2 sin(81x² + 81y2) dA, where R is the…

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Q: Use a computer algebra system (CAS) to evaluate the following integral. dx √2² x² + 6x + 73

A:

Q: The answer is incorrect, can you please revise your work? Thank you.

A: To find the partial derivative of the function at the given point

Q: Solve the initial value problem, and graph the solution function x(t). x' + 8x' + 16x= 1+S(t-5);…

A: First we have to solve given initial problemx''+8x'+16x=1+δ(t-5);       x(0)=x'(0)=0

Q: 7) g(x) = arctan (3x³)

A: Given the function is: g(x)=arctan(3x^3) We need to find the power series of g(x) and the interval…

Q: Find the amount accumulated FV in the given annuity account. (Assume end-of-period deposits and…

A:

Q: Solve the following equations for exactness, then solve:  1. [2xy cos(x2) - 2xy + 1] dx + [sin(x2)…

A: The given differential equation is:2xy cosx2-2xy+1 dx+sinx2-x2 dy=0

Q: Determine the outstanding principal of the given mortgage. (Assume monthly interest payments and…

A: We have to determine the outstanding principle of given mortgage.

Q: Consider the function f(x) = 12x5 + 60x¹ - 100x³ + 1. f(x) has inflection points at (reading from…

A: The function is  f(x)=12x5+60x4-100x3+1

Q: Use Euler's method with step size 0.5 to compute the approximate y-values y1, 92, 93, and Y4 of the…

A:

Q: (В y (62 - (52²-2³)) dz [² (62 − (52² − 2³)) dz + S* ((52² − z³) − 6x) dz 15+ 10+ 5 10 1 2 3 The…

A: Given data

Q: a. What is the partial derivative of this Hamiltonian with respect to x? b. What is the partial…

A: