Use polar coordinates to find the volume of the given solid. Inside the sphere x² + y² + z² = 16 and outside the cylinder x² + y² = 1

Q: Calculate approximations of tan(π/4-0.1) by using Taylor polynomials P₁(x), P2(x), P3(x). Use c=π/4.…

A: The given function is fx=tanπ4-0.1 To find: P1x, P2x, P3x about the center c=π4.

Q: Ö Surface Aren 14/₁ 2² (6²-y²) => y=b₂ √²-² S2x $(1) JH (FW))" 0 $(x)=b √a²-x² => g² (x)=√ D n So…

A: From the above details we have,

Q: F(x)= (beta*x)^y G(x)= (1/x^2) F(g(x))= ? F’(g(x))=?

A:

Q: If Y = f(x) = 6/x^3, find dy/dx? Select one: O a. (-18)/x^4 O b. (-9)/x^3 O c. 6X^2 O d. 18x^3

A: Sol:- Given:- Y=f(X)=6X3

Q: convergence. a. Σ Ξ (-1)"x2n b.00 3"

A: Ratio Test for convergence of a series . Series ∑an is convergent if limn→∞an+1an<1

Q: Find the solution of the initial value problem y" + 4y' + 5y = 0, Y (²) = 0, y' (²) 7. y(t) = How…

A:

Q: very C

A: Given as, F:X→Y be linear. Cauchy sequence  Fxnis Cauchy in Y.

Q: Solve the given initial-value problem. y(x): = y" + 6y' - 7y = 11e2x, y(0) = 1, y'(0) = 1 -7.x 2x 7e…

A:

Q: 1. Find the inverse Laplace transform y(t)=L−¹[Y(s)] where (b) Y(s)-e-³s (25-3) $²-49

A: We will be using the formulas of inverse Laplace L-1{a·fs+b·gs}=a·L-1{fs}+b·L-1{gs} L-1{1s-a}=eat…

Q: Find the indefinite integral. sin4 60 de Step 1 To find the integral 1 - cos 2x Rewrite the…

A: The answers are as follows

Q: Solve y" - 2y + y = 12e³t y(0) = -1 y'(0) = 0

A:

Q: Solve for X. 2-[ X = -5 X + -41 = 9 X.

A: The given problem is to solve the given matrix equation and find the matrix of X.

Q: Let f be a function with 2 + 3i as the only singular point of it. If 2 + 3i is a removable…

A: Given f be a function with 2+3i as the only singular point of it. If f is a removable singularity of…

Q: 6. Which of the following is false? a. If the series Σn an converges, then lim a, = 0. 818 b. If lim…

A: Only Option C is False.

Q: Find the solution of the given initial value problem. y(4) - 8y" + 16y" = 0; y(1) = 10 + e¹, y'(1) =…

A:

Q: . Using Green's theorem, show that the area of a plane region in polar coordinate is 1 $ C r²do.…

A:

Q: Solve the initial value problem y" +0.2y +0.01y = 0; y(0) = 0, y/(0) = 2

A: We will 1st find roots of characteristic equation . depending upon type of roots of characteristic…

Q: use bisection method not quadratic formula

A:

Q: (b) Use the comparison test to determine whether or not the integral +00 1 x4 + ex dx converges.

A: We have to determine whether the following integral converges or not by using comparison test :…

Q: Question 5 1 Q.5.1 Determine whether (-pVq) A (q→ -r-p) A(pVr) (denoted with p) is satisfiable.

A:

Q: There are 860 freshmen. If that is 43% of the class, how many are in the class?

A:

Q: 1. (a) Find the Fourier series of the function f(x) = 1 |x|, -2<x≤2 (b) Hence prove that 1 + 3/2 +…

A: 1. (a) Given,                 f(x)=1-x, -2&lt;x≤2

Q: Spectral Decomposition

A: We solved by spectral decomposition to orthogonally diagonalized the matrix A.

Q: Make a generalization if tbe patterns discovered from the answers on the table.

A: Introduction: In mathematics and number theory, the Fibonacci sequence is one of the most important…

Q: Estimate the following definite integrals using the Trapezoidal rule and Simpson's rule. Estimate…

A: Given integration is I=∫0πsin(t)dt Here  f(t)=sin(t) n=4 So length of subinterval is…

Q: |3z +48z = 5 cos(4t) |3z +53z5 cos(4t) |3z +25x' +48z = 5 cos(4t) ✓3r |3x +22r' +48z = 5 cos(4t) |3z…

A: solution is given below:

Q: I. Modified TRUE or FALSE. Write Tolits if statement is true and Tol if statement is false. For…

A: 7. False  Because Modus tolens is a law of inference.

Q: Consider the function To/R₂ [x] →> R₂ [x] given by T (a+bx+cx²) = (a +2b) + (C+2a) x + (c+1)x² Prove…

A:

Q: Approximate (1.999) by using linearization.

A: The linear approximation of a function fx at a point x=a is given by the formula fx≈fa+x-af'a Where…

Q: Find the general solutions of the linear, homogeneous differential equations subject to the given…

A: Given DE is y"-3y'-4y=0 .......(1)  y(0)=4,y'(0)=1

Q: Prove that Z(Sn) = {e} for n ≥ 3.

A:

Q: Consider the set S of primes less than 15. List the set S . (Input this as a list with no spaces,…

A: Disclaimer: Since you have posted a question with multiple sub-parts, we will solve first three…

Q: Compute с -ater-clockwise see from above. where xdy - y dx ус is the unit circle center at origin…

A: Introduction: In vector calculus, another very important theorem is Green's theorem. It makes a…

Q: Find the indefinite integral using each method. (Use C for the constant of integration.) x³ √ √ 3 +…

A:

Q: Set-up the integral that would find the volume of the solid of revolution when given region bounded…

A:

Q: do

A: As per our guidelines only first three subquestion are solved. For remaining subquestions kindly…

Q: Let = . Let S be the triangle with corners at (3, 1, 2), (3, 4, 2), and (0, 4, 2), oriented away…

A:

Q: Show that if s(3) 4(q- _9−2+9(1+ 93 2(g-1) increasing or decreasing. For 3 > 0, q> 3

A: The given function is                               sβ=q-2+q1+4q-1qβ122q-1 where β&gt;0 and q&gt;3.…

Q: Find the Taylor or McLaurin series for the following functions f(x) = xe-*, a=0

A: Here f(x)=xe-x,a=0. We find the Maclaurin series of f(x).

Q: where do the curve of y = cosx and y=x²-1 intersect?

A: We have to find the point of intersection of the given equations. First we will sketch the graph of…

Q: Prove that the 2nd smallest non-abelian simple group is of order 168.

A: Introduction- An abelian group, also known as a commutative group, is a group in abstract algebra…

Q: Q4/ For the function f(x) = 2x + x²-3x³ +6, answer the following: a. What are the critical points…

A: We are given a real valued function f(x)=2x+12x2-13x3+6 to answer the each part we will use the the…

Q: y" - 2y + y = 12e³t y(0) = -1 y'(0) = 0

A: First you will form the general solution by finding the complementary solution and then particular…

Q: Find the inverse of AB if 5 -1 A-¹. and B-1 = -5 -5 5 4 [84] 0 -1 (AB)-¹ = E

A:

Q: Answer the following questions for the function defined on the interval [-5, 7]. a.) f(x) is concave…

A: Given:  f(x)=xx²+1

Q: 3 (i) Given that 3x³ +5x2 + px+8 = (x-2)(ax² + bx + c), find the value of each of the integers a, b,…

A: Here given that 3x3+5x2+px+8=x-2ax2+bx+c We have to find the value of the integers a, b, c, p and…

Q: A furniture manufacturer estimates that the weekly cost of manufacturing x units of a particular…

A:

Q: Let f: C¹[0, 1] - → K be defined by f(x) = x¹(1), x € X. Consider the sequence {Zn} in C¹[0, 1]…

A:

Q: Name find the of each figure 130. units 2

A: # as per the guidelines we are entitled to solve one question (maximum 3 subparts) . Please resubmit…

Q: Set-up the definite integral that would compute for the Moment of Mass about the x-axis of the…

A: To Set up: The definite integral for the Moment of mass about the x-axis of the region bounded by…