Question 1 [3 a) { exact: 1: Verify that the differential equation is (cos(x)+2x + y)dx+(− sin(y)+6xy5 )dy = 0. b) [ differential equation. Find the general solution to the above

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

A:

Q: Find the general indefinite integral. (Use C for the constant of integration.)

A:

Q: The given family of functions is the general solution of the differential equation on the indicated…

A:

Q: Find the component form of the vector u initial point (3,8,8) terminal point (5,6,10)

A: Initial point of u is (3,8,8)terminal point of u is (5,6,10)

Q: Use Taylor's Inequality to estimate the accuracy of the approximation f(x) ≈ T₁(x) when x lies in…

A:

Q: Evaluate 1) |x-2|dx

A:

Q: Find S н - 2+ dx

A:

Q: Evaluate the double integral. Sxy² da, D is enclosed by x = 0 and x =

A:

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

A: Since you have asked multiple question, as per company guidelines we will solve the first question…

Q: 7x (x+3)³ a. Find lim F(x). X-3 Let F(x)= b. Find the vertical asymptote of the graph of F(x). c.…

A: F(x)= 7x/(x+3)3  a) find the limit of F(x) when x tends to -3 .  b) find the vertical asymptote of…

Q: Given the function f(x) = x² – 3x f(2+h)-f(2) h (a) Find the expression (b) Use your result from…

A: The given function is ; f(x)=x2-3x.

Q: Question 5 Test the series below for convergence using the Root Test. 5)₁ ∞ n=1 f(n): 3n 6n + 5 The…

A:

Q: A function is given. f(x) = x³ 3x²; x = 0, x = 10 (a) Determine the net change between the given…

A:

Q: 2) × 2+4i 3+1 and 2=3-1 2+i 2 prove that x² + 3xy + y² = 6 if it was

A:

Q: Solve the following differential equations: a- (2x + 3y -2) dx + (3x -4 y +1) dy=0 b- (x²+3y²)…

A: The given differential equations are;  1) (2x+3y-2)dx+(3x-4y+1)dy=0 2) (x2+3y2)dx-2xydy=0.

Q: Find the derivative of the function. (x-7)(x²+2x) +3 y = O A. OB. dy dx O D. dy dx dy O C. dx dy dx…

A:

Q: Consider an exchange economy with 2 consumers, A and B, and 2 commodities, x and y. Each consumer is…

A: Multiple subparts are asked, I am answering first 3

Q: Use L'Hopital's to determine the limit. lim 0 0 1 1-cos x I O sin x COS X as x approaches 0

A:

Q: Use the graph to find the point(s) of inflection of f. (Give your answer in the form of a…

A: Given: the graph is given we want to find inflection point and concave down range         Inflection…

Q: 7. Use the Method of Lagrange Multipliers to find the extrema value of a function f(x, y, z) = 2x² +…

A: Concept: Lagrange multipliers: A straightforward and elegant technique for determining the local…

Q: √2x+6 2. Y = √√√3x² +10x +3

A:

Q: 2. A circular cylindrical hole is bored through a solid sphere, the axis of the hole is being a…

A:

Q: 1. y = x-3 2x³+x²-18x-9

A: As per our guidelines we are supposedly to  only one question. Kindly repost others question as a…

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

A:

Q: nd an equation of a plane passing through the following 3 points (1,-1,-1), (-4,1,4), (3,5,3)

A: topic- equation of plane through three points equation of plane passing through three points…

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

A:

Q: 10. Let w = f(x, y, z) = xe. If x = t², y = 1-t₁ z = 1 + 2t, use the partial dw dt derivatives and…

A: Using the chain rule and rule of partial derivative and get the required derivative.Final solution…

Q: = Find the area of the region bounded by the curves y on the interval [0, 1] as seen in the shaded…

A: This question can be solved using the concept of area bounded by curves.

Q: (a) lim x² - x + 6 X2 x 2 x² + 2x - 3 x² (b) lim x - 6 x 3 x² - 2x - 3 x - 4 (c) lim x+4√√√x-2

A: a.limx→2x2-x+6x2+2x-3=4-2+64+4-3=85b.limx→3x2-x-6x2-2x-3limx→3x-3x+2x-3x+1limx→3x+2x+1=54

Q: Use implicit differentiation for x² + y² O x/y O 5x O-x/y O -5x = 25.

A: To find the derivative.

Q: Let D be the planar region bounded by y = 0, y = x², and x = 1. The integral ff cos(z² + y²) dA…

A:

Q: Write an equation for the function graphed below -7 -6 y = -5 -4 -3 Get help: Video 5 4 3 2 1 -2 -3…

A:

Q: Use the remainder theorem to evaluate the polynomial for the given values of x. g(x)=6x³-7x²-36x+42…

A:

Q: Two particles move along a straight line. The first particle, Particle A, travels with a velocity of…

A: Solution is given below:

Q: Solve the initial value problem 25y" — 40y' + 16y = 0, y(0) = 2, y'(0) = 3. y(t): How does the…

A: We can solve this as follows:

Q: Find the radius of convergence, R, of the following series. Σn!(7x - 1) n = 1 R Find the interval,…

A: Here we have to find the radius and interval of convergence.

Q: Use the figure below to find the exact value of the trigonometric function of angle A. sin(A) 00 7 A

A:

Q: Determine whether the improper integral diverges or converges. 16 1 √√√x dx converges diverges…

A:

Q: B. Solve one of the following inequalities. Write your answer as an interval or union of intervals.…

A: Please see the answer below.

Q: Evaluate cos/dx 2 1) co S

A:

Q: Solve the initial value problem 25y" - 40y' + 16y = 0, y(0) = 2, y'(0) = 3. y(t) = How does the…

A: We have to solve the initial value problem 25y'' - 40y' + 16y = 0 y(0) = 2 & y'(0) = 3

Q: use triple scalar product to find the volume of the parallelpiped u= v= w=

A:

Q: Write a polynomial f(x) that satisfies the given conditions. 2 Polynomial of lowest degree with…

A:

Q: dx Evaluate So x²+4

A: Follow the procedure given below.

Q: Given that f(x) = h(x) x5 f'(-1). Show your work. -, h(-1) = 4, and h' (-1) = 7 find

A:

Q: he following represents the dor 4- x² - y² ? (C) y x Y X

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

Q: 6. Find complementary function and particular integral of the following differential equation: (D- d…

A:

Q: 2: io ue Approximate the area of the region bounded by the graph of f(t) = cos (t/2-5/8) and the…

A:

Q: A. Find the following limits. Answer four only. x-¹-1 i. ii. iii. lim- X-1 X-1 lim 4x-x² X-4 2-√√x…

A:

Q: Transform the given differential equation into an equivalent system of first-order differential…

A: Using substitution and differentiation,