Use double integration to find the volume of the solid bounded by the cylinder x² + y? = 16 and the planes z = 0 and z = 4 – x. NOTE: Enter the exact answer. V =

Q: #3 Evaluate F. dr. F(x, y) = 3xi + 8yj C: r(t) = ti + V4 - t²j, -2 st< 2

A: Given problem:-

Q: Using the Nth term test for divergence 5 1 n=1_2n +14 5 diverges since lim is equal to 1 2n+14 O 1/3…

A: We can answer the question as below.

Q: For the given vectors a and b, find the cross product a x b. =(3,0, -1), b = (3, 2, 0) a %3D a x b =

A:

Q: Express the integral as an equivalent integral in which the z-integration is performed first, the…

A: Integral

Q: 1. The sum of the digits of a two digit number is 15. One-third of the number diminished by 12 is…

A: A detailed solution is given below.

Q: Solve the differential equation Bernoulli Equations: (x² + y²)dx – xydy = 0

A:

Q: -sin (In x?)ecos² (In x) dx 100x2-x2e2 cos (In x)

A:

Q: Find each of the two areas bounded by the

A:

Q: ind the arc length oI the parametric curve. 0 = 6 cos (t), y = 6 sin(t), z = 8t; 0 stST

A: Given: x=6cost, y=6sint, z=8t

Q: Find the sum of the first n terms of the following arithmetic sequence. a1 = 2, d = - 4; n = 6 O A.…

A: Given problem:- a1 = 2 ,d = -4 ,n=6  To find:-  Sum of n terms of given arithmetic sequence

Q: If f (x)= [a(«) =os* '(5) [1+ sin(t?)] dt find f 1 dt, where g(x) V1+t3 COS X

A: We need to find value of derivative.

Q: 2. Determine the area of the region bounded by the curve y = x³ – x² – 2x, and а. the x-axis b. the…

A: This is a problem related to area calculation using integration. Please find the procedure given…

Q: 1.) ° 6x3+4x²-8x dx I. Evaluate the following Definite Integral. 1.) ° 6x³+4x²-8x 2.) x²(2x3 + 1)Fdx…

A: we want to find the integral ∫03( 3x-6 -1 )  dx

Q: Express the integral as an equivalent integral in which the z-integration is performed first, the…

A:

Q: (2))? dz: Consider the indefinite integral a) This can be transformed into a basic integral by…

A:

Q: Find the Taylor series for f(x) centered at the given value of a. [Assume that f has a power series…

A:

Q: Find the polar equution for the cartesian curve r=8 sin o Cos o r=8 sec e tan E r=8 sine tan E r=8…

A:

Q: 47. f(x) = V(3 – x) on [1,3]

A:

Q: II. Find the Inverse Laplace of the following 2s-9 d. s2 +2 1 е. (s²+1)(s²+4s+8)

A:

Q: Numerical Integration (Simpson’s) 1. Using the Simpson Three-Eights method, at n = 6, what is the…

A: According to barteleby guidelines I can only answer the first question of the three given. Please…

Q: 3.) ž sin'(x)dx

A:

Q: In series RL circuit, L=4 henry, R=100 ohms and E =200 volts, find the value of current when t =2…

A: Given ; L= 4 henry , R=100 ohms and E=200 volts , t= 2 sec

Q: Find the general solution 5. (D² – 1)y = 0

A:

Q: INDETERMINATE FORMS: Evaluate the limit by employing Theorem 23. f(x) F(x) f'(x) lim = lim Еquation…

A: This question is based on L hospitals rule.

Q: Evaluate the line integral along the path C given by x = 4t, y = 8t, where 0 <ts 1. / (x+ 3y²) dy #4

A:

Q: Solve for k such that 1 | k(x² – 2x + 1)dx = 5

A: Given problem:- ∫ k(x2 -2x+1) dx =5  Solve for k

Q: )Solve for k such that 1 k(x2 – 2x + 1)dx = 5 - 0.

A:

Q: 465.98 23.98 2.789 56.09 ATATA TTA TA

A: Rounding up

Q: Find the area bounded by the curve r= 2+cos θ

A: Given problem:- Find the area bounded by the curve r= 2+cos θ

Q: 28) In Problems 28 and 29, given the IMPORTANT FORMULA x(a+1)+ C (if a2 -1) and x1 dx = In x + C.…

A:

Q: II. Find the Inverse Laplace of the following 1 a. s² +6s+25 s2 b. (s-1)3 7 C. s4 8 - - - s3 s2

A: According to bartleby guidelines when student post multiple subpart questions then expert must have…

Q: e* dx V1-e2x

A: Topic = Integration

Q: Find the particular solution of the DE y''-11y'+24y=0 when y(0)=2 y'(0)=-3

A:

Q: The sum of the digits of a three-digit number is 11. The tens digit is three times the hundreds…

A: Let a be the hundreds digit, b be the tens digit and c be the units digit. Thus our required three…

Q: Jo 4 +t°

A:

Q: ||r(t) × r"(t)|| Use the formula k(t) to find k(t). ||r(t)||* r(t) = 8 cos(8t)i+ 8 sin(8t)j + 5tk…

A:

Q: Solve the differential equation Integrating Factor by Inspection: (xy – 2y?)dx – (x² – 3xy)dy = 0

A:

Q: 1. Find the particular solution of the DE y" -11y' + 24y = 0 subject to the boundary conditions y…

A: The differential equation can be solved as follows:

Q: Answer is incorrect

A: Apologies for the inconvenience. In the second last line there was a calculation mistake.

Q: 22. (x+1)v2r-1 dr

A: Note: According to our expert guidelines only one individual question is to be answered kindly…

Q: Q1: Find the length of a and b in the following triangle a 75 30

A:

Q: VI 23) Consider the region in the second quadrant between the ciréies X²+y?=4ard x?7y==25 ?-25, and…

A:

Q: Find the Taylor series for f(x) centered at the given value of a. [Assume that f has a power series…

A:

Q: Find the Maclaurin series for f(x) using the definition of a Maclaurin series. [Assume that f has a…

A:

Q: Find the limit. NOTE: Enter the answer using round brackets. t2 + 8 1 lim t→+∞\ 5t2 +6' 8t (?, ?)

A: To evaluate the following limit.limt→+∞t2+85t2+6, 18t=?, ?

Q: ||r'(t) × r"(t)|| Use the formula k(t) to find k(t). 3 ||r(t)||³ r(t) = 3 cos(2t)i+ 3 sin(2t)j + tk…

A: The given formula is: κt=r't×r''tr't3 And rt=3cos2ti+3sin2tj+tk   As we know that; The Chain rule;…

Q: Use Green's Theorem to evaluate the integral. Assume that the curve Cis oriented counterclockwise. 2…

A:

Q: Barbara put P100 into banks savings account. The account accrues a 9% interest rate compounded…

A: Given: Amount =P100 . Rate of interest= 9%  Time n= 12 years

Q: 19. e dr dr 4 – 2² 20. dr 21.

A: 19.)∫1∞e-xdx=-e-x0∞=-e-x0∞=-e-∞-e-0=-0-1=1∫1∞e-xdx = 1

Q: Find div F and curl F if F(x, y, z) = 3e™Y i– 3 cos yj+ 10 div F=

A: Given: 3exyi-3cosyj+10sin2zk