B: By using Homogenous method solve the first order differential equation (1+ e») dx - ely (G-1) dy = 0

Q: Find the arc length L of the graph of r(t). 1 .3 r(t) = i+t j+¬V61² k, 2 <153 L =

A: Solve the following

Q: Evaluate the integral by first reversing the order of integration. NOTE: Enter the exact answer. 5…

A:

Q: 3 The series E converges if n=2 (n+ 1)P (n – 1)ª (a) p+q1 (c) p+q=1 (a) p+q=2 (e) -1<p+q<1

A: Solve the following

Q: Evaluate the double integral f(r, 0) dA. -7 cos(0) r dr de 497 2 Sketch the region R. 7/2 A/2 6 2 4…

A:

Q: Let f(x) = 10x° + rx? + e2x. Compute f(")(x). (Use symbolic notation and fractions where needed.)…

A:

Q: Use Green Theorem to Evaluate y x²dx – x²dy where C is left half of x² + y² = 25 %3D

A:

Q: k lim (1+†) k→∞ k

A: We have to find limit

Q: Use the formula k(t) : ||r() × r"(t)|| to find K(t). %3D r(t) = t²i + t®j %3D

A: Given that,     r(t)=t2i+t9j

Q: Find the arc length of the parametric curve. x = 24 cos(t), y = 24 sin(t), z = 7t; 0<t< T L

A:

Q: If f(x) t*dt then 0. f'(x) ||

A:

Q: Find the directional derivative of f at P in the direction of a. f (x, y) = 17 tan Р(-18, 18); а %3D…

A:

Q: Find the volume of a cap of a sphere with radius 50 and height h = 3.

A: volume of sherical cap with radius given r=50 and height=3

Q: 258. A spherical balloon is filled with air at the rate of 2 cu cm/min. Compute the time rate of…

A:

Q: 10. Determine if the series converges or diverges using a Comparison test based on a Taylor…

A:

Q: Choose the correct word to fill in the blank for the following theorem. "If f(x) is on [a, b), then…

A: To solve the following problem

Q: A particle moves along a straight line with equation of motion s = f(t), where s is measured in…

A: This is a problem related to derivative of the function. Derivative of the distance function give…

Q: Let 7. B(t) = ift < 2 - Vt+c ift 2 2. Find the value of c so that lim B(t) exists. t+2

A: This question is based on limits.

Q: Determine the general solution to the vector differential equation r' = Ax with A = [2030-40 -30 2]…

A:

Q: 3x 4x e, y = e", and Sketch the region enclosed by y = x = 1. Find the area of the region.

A:

Q: Find the limit. lim (t i - 8 j+ 1? k) k lim (t i-8 j+t k) = j+ i i+ i 1-2

A:

Q: 17-22 Use appropriate forms of the chain rule to find əz/du and əz/əv. I 17. z 3D 8x*у - 2х + 3у; х…

A:

Q: Find f, and f, as functions if 2y f(x. y) = y+ y + cos x

A: This question is related to differentiation, We will solve it using given information.

Q: Find the length of the curve r(t) = t^2i − 2√2tj + (t/2 − 1)k for 0 ≤ t ≤ 1.

A:

Q: Use a double integral to find the volume of the indicated solid. 9. z = 9-2 y 2. y=2 4 X=4

A:

Q: The current population of a certain bacteria is 5410 organisms. It is believed that bacteria's…

A: Given, Initial population (P)=5410 , Rate of multiples (R)=3 , Triplet in 9 minutes. Therefore n=9…

Q: The region bounded by the given curves is rotated about the specified axis. Find the volume of the…

A:

Q: Solve y" +3y'+2y =

A:

Q: OGraph the following Runetion two -4

A: Graph

Q: Use the method of cylindrical shells to find the volume generated by rotating the region bounded by…

A:

Q: Q1: Find dy/dx of the following functions: 1. x'e? y = log2 2Vx+1 2.

A: As per the company guidelines We can first question only. Please understand. Kindly repost the…

Q: Sketch the region enclosed by the given curves. Decide whether to integrate with respect to x or y.…

A: Let's find.

Q: Prove that f : [−4,2] → R defined by f(x) = 7/x+5 is uniformly continuous on the interval [−4, 2]…

A:

Q: prove that if the polynomial f(x) = x2n + a1x(2n-2)  +....+an-1x2 + an  is divisible by g1(x)= x-1…

A: prove that if the polynomial f(x) = x2n + a1x(2n-2)  +....+an-1x2 + an  is divisible by g1(x)= x-1…

Q: Find the domain of r(t) and the value of r(to). NOTE: Round your answer to two decimal places when…

A:

Q: 5. Evaluate the limit of (x^3-2x^2-x+2) /(x^2-4) as x approaches 2. a. a b. % с. 2/5 d. 4/7

A: Note: Since the student has posted multiple questions but first question (question number 4) is…

Q: Find a power series for the function, centered at c. 1 h(x) 1 C = 0 8x' h(x) = n = 0 Determine the…

A: We have to find the power series and interval of convergence.

Q: Find the volume of the solid obtained by rotating the region bounded by the given curves about the…

A: Given region is bounded by the function y=16x-2x2 and y=0 and rotating about y axis.

Q: Calculate the (f(g(x)))' and (g(f(x)))' derivatives if f(x) = x7 1 g(x) 5x + 1 (Express numbers in…

A:

Q: Find the extremum of f(x,y) subject to the given constraint, and state whether it is a maximum or a…

A: In this we use Lagrange multiplier to find out max/min value for given constraints, so I'm providing…

Q: Q1) Suppose w = x = cos? t, y = sin? t, z = dw Evaluate at t = 3, by using the Chain Rule dt

A:

Q: . The line segment from (1, –1,3) to (0, –3, 1) forms a diameter of the sphere S1. Find the…

A:

Q: Given the following functions: f(x) = cos(x) g(x) = x'7 + 1 Find f(g(x)) and (f(x). (Use symbolic…

A: The given functions,  fx=cosx  gx=x17+1

Q: f(x) = lnx/sqrt(x) find the following: first derivative: Intervals where f is…

A:

Q: Where is each function continuous? (b) f(r) = sin-(1-r) %3D I+3 (c) f(r) In ) %3D (d) f(r)= 12+5r+ 6

A:

Q: Set up the definite integral required to find the area of the region between the graph of y = r - 11…

A:

Q: Evaluate the iterated integral. 6 7 8 /// (x² + y² + z²) dxdydz -6 0 0 6 7 8 (x² + y² + z?)dxdydz i…

A:

Q: lim x-00 1 with a a real constant different from 0, consider the Consider the limit following…

A: We have to find out the correct answer

Q: Find the derivative of the function at Po in the direction of A. g(x, y) = x - (y/x) + V3 sec-…

A: Given problem:-

Q: Sand falls from a conveyor belt at a rate of 10 m^3/min and accumulate in a conical pile with the…

A: Use derivative concept

Q: dy is dy xy dx dx The general solution of y² + x² "

A: Solution is given below: