1. Find the general solution to the DE ye 2x (4+e ²*) dy = 0 dx

Q: A child enters a carousel that takes one minute to revolve once around. The child enters at the…

A: Concept: Starting from the point (0,1) a child circles around counterclockwise If it takes 1minute…

Q: 6. Find the linear approximation to f(x) = ² at a = 4.

A: The objective of the question is determine the linear approximation function for given function at…

Q: dy dx + ² = y² dx x (Bernoulli's equation)

A: Solution

Q: 12. Suppose that lim g(h) = L. h-0 a) Explain why lim g(ah) = L for any constant a 0. h-0 b) If we…

A: Let's solve limit problem.

Q: 13. r(t) = e'(cos ti+ sin tj + tk) sto

A: Topic:- application of derivatives

Q: A company's cost function is C(x)=√√9x² + 1600 dollars, where x is the number of units. Find the…

A:

Q: (A) The integrating factor for (2y - xy²)dx - (3x+x²y)dy = 0 is 5 2xy 5xy

A: If a differential equation Mx, y dx + Nx, y dy = 0 has the form f1xy y dx + f2xy x dy = 0 and if…

Q: Consider each problem Problem A Jack has $800 invested in two accounts. One pays 6% annual interest…

A: Topic- Simple interest Note: As per bartleby guidelines, we are supposed to answer only first…

Q: Find the absolute extrema of the function on the closed interval. minimum y = 7 cos(x), maximum…

A:

Q: dT Consider the differential equation x +T=e* with 7(0) = 1. What is the approximate value dx of…

A:

Q: (a) Draw the vectors a = (4, 3), b = (2, -1), and c = (9, 1). y 10r 10 5 5 p po kap -10 5 -5 5 10…

A: (a)  to draw the vectors a=(4,3)   b=(2,-1)      c=(9,1)

Q: estimated

A: Given: P(t) = 13.86t0.535 Where, P(t) = percent of the population t = time in year since 2011

Q: 1. Find the solution of the given initial value problem. y" + 2y + 2y = 0, y(π) = −1, y'(π) = 0.…

A: Given, the differential equation is Y''+2Y'+2y=0 Now, the differential equation can be rewritten…

Q: Check that the four points P(2, 4, 4), Q(3, 1, 6), R(2, 8, 0), and S(9, 2, -1) all lie in a plane.…

A: Given points : P(2,4,4), Q(3,1,6), R(2,8,0) and S(9,2,-1)

Q: Evaluate with the Simpsons rul

A:

Q: In Exercises. the region. 37. 3 2 ), use an iterated integral to fi y=4-x² X

A: Topic:- Calculus

Q: (A) (В) Ⓒ du Which of the following is the general solution of www.dx u² + 2x² = C xu² +u = C…

A:

Q: Given the functions f(x) = 3x - 1 and g(x)= answer the following (simplify all answers as much as…

A:

Q: 1. Asymptotes at y = 5/3x - 29/3 and y = -5/3x + (11/3 and a vertex at (1, -3).

A: Given find intersection of asymptote , which is center of hyperbola ( h , k ) = ( 4 , -3 )   one…

Q: 3. Find the area of the region enclosed by the line y = x - 1 and the parabola y² = 2x + 6. Graph…

A: Solution is given below:

Q: (c) Give one example where the Green theorem fails, and explain how.

A: Green's Theorem

Q: - Which of the following is the general solution of 2 - y secx = y³ tanx ? dx

A:

Q: Given (13, 8) and (x,- 7), find all x such that the distance between these two points is 17.…

A: given points(13,8) and (x,-7)

Q: lim x->4 4 1 √x-2 x-4

A:

Q: In Exercises the region. , use an iterated integral to find the area of 36. y 3- 2 (1,3) (2,3) (1,…

A:

Q: 8. Let s(t) = 2t² - t + 1 be the position of a particle from its starting point, in meters, after t…

A:

Q: d. e. Σ(**) - η 4k Τύπος (Σ(44)) - lim η-400 η k=1 - A C

A:

Q: T Use Trapezoid rule to approximate the value of [sin xdx. Use four 0 subintervals. Express your…

A: Topic:- application of integration

Q: Consider a function z = F(u(s, t), v(s, t)) where F, u, and v are differentiable and u(12, 8) = -12,…

A:

Q: Find the vertex, focus, and directrix of the parabola given by the equation. (x - 3)² = 4(y + 1) (x,…

A:

Q: The strength of a patient's reaction to a dose of x milligrams of a certain drug is R(x) = 8x√16…

A:

Q: Examine the following four equations and the graphs labeled i, ii, iii, and iv. Determine which…

A: (a)  y-32=x-5

Q: Question 9 Two vectors have the following magnitude, A= 10.1 m and B = 9.7 m. Their vector product…

A:

Q: valuate the integrals for f(x) shown in the figure below. The two parts of the graph are…

A: Given query is to find the value of the integral.

Q: [₂ (1-x-4x³. -2 •3 0 0 (1 − x − 4x³ + 2x5³) dx (5 + 3 cos x) dx 3 x² ex dx

A: Given that  some integration and we solve these integrations by using general property of…

Q: Consider the differential equation x +T=e* with 7(0) = 1. What is the approximate value dx of T(2)?

A: Given, xdTdx+T=ex with T0=1 We have to find the approximate value of T(2).

Q: A tank initially contains salt in the pores if inert material and 10 gallons of fresh water. The…

A:

Q: Line 1: 3x - 5y = 15 Line 2: a line perpendicular to 3x - 5y = 15 that contains the point (3, -5)…

A: solution is given ...

Q: f(x) = {in(atsine) at find f'(x)

A:

Q: (b) x + 2y = 4x², y(1) = 1 dy dx dy (c) 3x²y = xe*³, y(0) = 1 dx - -

A:

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

A: Explanation of the answer is as follows

Q: Which of the following is an integrating factor for ydx - xdy = 0 ? ...

A:

Q: 3s +4 F(s) = s(s± + 6s +13) 2

A: Explanation of the answer is as follows

Q: write 20190 as a mixed fraction.

A: Given question:- write 201/90 as a mixed fraction.

Q: The sales of a new high-tech item (in thousands) are given by the following function, where t…

A:

Q: Find the center, vertices, and foci of the ellipse given by the equation. 2+2-1 16 4 center (x, y) =…

A:

Q: dy ng is the general solution of xln x + y = ln x² dx y = lnx + C y = lnx+₁x

A: We have to choose the correct option from the given options according to the given information

Q: A B -3 2 The non-zero value of n for which the differential equation (3xy² + n²x²y) dx + (nx³ +…

A: The objective of the question is determine the value"n" for which the given differential equation is…

Q: Find the parametric equation for the line where the planes 2x - 2y + 8z = 24 and 10x − 3y + 6z = 18…

A:

Q: 3 S(2²=-1) ³ x dx

A: Given query is to find the integral.