Below is an image to calculate the surface area of a sphere using dA. I can see how rcosθdϕ works, but I don't understand how that side can't just be rdϕ with a slanted circle representing the arc length. The second part I don't understand is why it is integrated from π/2 to -π/2. See attached image.

Q: Let y = Lal: Let L be the line spanned by u. and u %3D Write y as the sum of two orthogonal vectors,…

A:

Q: 2. Let f : [a, b] R be a bounded function. Prove that if f is continuous at ro € [a, b), then L(|f])…

A: Here we use the property of continuty.

Q: What modifications would have to be made to find the derivativesin e ife is given as an angle in…

A:

Q: The task is to find the local linear approximation of V2 3 g(x,y) = +cot (x +5). TT at (1, –1) to…

A: Local linear approximation of f(x, y) at the point (a, b) is given by Lx,y=fa,b+fxa,bx-a+fya,by-b

Q: Solve: (dy/dx)? + (y– 1– (x/y)) dy/dx – x/y(y – 1 ) = 0

A:

Q: et Determine if the improper integral dx converges or diverges. (1 - e)2 If it converges, find its…

A:

Q: aluate L(t(uo - u) +tu,}.

A:

Q: ,2 COS“ N cos“ n In n n2 n3 n=1

A:

Q: Q1) Evaluate the integral dy dx using polar coordinate

A:

Q: Use Newton's Method to approximate the zero(s) of the function. Continue the iterations until two…

A: Given is a function f(x)   First we have to find the root of the given function by Newton's method…

Q: (a) By reading values from the given graph of f, use four rectangles with heights corresponding to…

A:

Q: Find the present value of an annuity of $2000 per year at the end of each of 10 years after being…

A:

Q: 12 10 14 11 13 Consider the graph given above. Use the sorted edges algorithm to find a Hamiltonian…

A: Sorted-Edges Algorithm:   1. Sort the edges from lowest cost to highest cost 2. Add edges to your…

Q: Let A be a 2 x 2 symmetric matrix satisfying A = 12 and 3 with the spectral decomposition le A = 12…

A:

Q: Suppose that is an eigenvector of a matrix A with corresponding eigenvalue 8. Then x is an…

A: Eigen values corresponding to the eige equations.

Q: Find the smallest number n of terms needed to obtain an approximation of the series k=1 accurate to…

A: We have to find the smallest number n of terms needed to obtain an approximation of the series.

Q: (x² + 2x) cos(2x) dx

A:

Q: The given vectors form a basis for R3. Apply the Gram-Schmidt Process to obtain an orthogonal basis.…

A: The solution is given as

Q: O *SimpleTripjava - Notepad File Edit Format View Help Ln 31, Col 1 100% Unix (LF) UTF-8 1 2 3 em 1.…

A:

Q: i need the answer quickly

A:

Q: 1.1 Show that if |z| < 1. then lim z" = 0. %3D 1.2 Show that lim Vn = 1.

A:

Q: e Newton's Method to approximate the zero(s) of the function. Continue the iterations until two x) =…

A: The given function is f(x)=x5+x-8 find f(-2) f(2)=25+-2+8=32+2-8=26 find f(-1) f(1)=15+1-8=+1+1-8=-6…

Q: Approximate the sum of the series by using the first six terms. n+1 6) n² n=1

A:

Q: 3 .3 n=1

A:

Q: rmine whether the following series converges or di If the series converges, determine the sum. n/2 1…

A:

Q: (-1)"n" sin" (4) 2n n=1 CS Samed with Camacarner

A:

Q: QI) Evaluate the integral dy dx using polar coordinate

A:

Q: メ1

A:

Q: Graph and find the Fourier coefficients of the following functions f(x): - 1/2 < x < Tt/2 T/2 < x <…

A:

Q: Find valume bounded by abave Z:4-20 and below by Z-xy 2.

A:

Q: Given: sinx = (-1)" (2n+1)! -x²n+1for x ER (-1)"(2n+1) y2n+1 Compute the exact value of the sum E=0…

A:

Q: Consider the following two ordered bases of R³: {{2, –1, –1), (–2, 2, 1), (5, –3, –2)}, {(0, 1, 1),…

A:

Q: Evaluate the following double integral over the region R by converting it to an iterated integral. e…

A:

Q: Consider the following two ordered bases of R?: {{1, –1), (-2, 3)}, {(-1, –2), (1, 3)}. B a. Find…

A:

Q: 1. (x² + 1)² dr

A:

Q: Q1\calculate x1, x2, xn from the following equations: -3x1 + 9x2 + xn = 2 5x1 - 2x2 + 3x,n = -1 2x1…

A:

Q: The approximation of xln(x + 3) dx using two points Gaussian quadrature formula is:

A:

Q: Let E be the solid inside the sphere a? + y? + z? = 8z and above the plane z = 4, and let S be the…

A:

Q: 1.: Reword the statement below as a theorem about graphs and then prove it. Assume that if A is a…

A:

Q: 3. 1 2 Let S = 3. 8. Which of the following statements describes the set S? The set is linearly…

A:

Q: 3-x Q1) Evaluate the integral * dy dx using polar coordinate

A:

Q: Let f(r) = . (a). Find the average value of f on [0, e]. Use six decimal places. (b). Use Newton's…

A: Given that fx=xex2 (A) To determine the average value of f(x) on [0,e]. (B) To estimate all points…

Q: xi = 2x1 – 5x2 x2 = 4x1 – 2x2 X1 (0) %3D 2, х2(0) — 3 2х1

A:

Q: QI) Evaluate the integral dy dx using polar coordinate

A:

Q: Find area inside autside r= I てニノ

A:

Q: O Prove that G(Vatienal number bers)is negrigibleset

A:

Q: 7. Using pelor cerdinale te sehe e llowiny integrals ) dydx dady

A:

Q: dx 3 x² (9x²-4) 2 CS

A:

Q: Section 6.2 p. 559/561 # 88 In the following exercises, differentiate the given series expansion of…

A: Here we use basic differentiation and power series expansion to find this.

Q: Write TRUE if the statement is always correct and FALSE if otherwise. (a) If an >0 for all n E N,…

A: