c. -1 |sech udu = 2tane" + C %3D tan (sinh u) + C -1

Q: If f(x) = x² +- k find k so that f has a critical number at x = = 3. а. 6 b. 27 с. 216 d. 54

A:

Q: dx Evaluate | x² + 2x +5 [(x+1)/] a. arctan +C arctan +C 4 [(x+1), |(x+1), с. arctan -C d. arctan +C

A: Let I is the value of given indefinite Integration.

Q: Please show your answer to at least 4 decimal places. Suppose that f(x, y) = xy. The directional der...

A:

Q: 2. A curve is defined by y = sin(2x), 1 < x < 3. i) Set up an integral for the length of the curve. ...

A: We are asked to setup the integral for the given

Q: 2. (2.xy – sin x)dx + ( - cos y dy = 0

A:

Q: Find the limit. Use l'Hospital's Rule if appropriate. If there is a more elementary method, consider...

A: We have to solve the limits

Q: Solve the following differential equations. Indicate the (Differential Equations) method/s used at t...

A:

Q: cot 2x 2. lim TC csc3x+tan x 4

A: To evaluate: limx→π4cot 2xcsc3x+tan x

Q: Determine the second derivative of y = V5x² + 1 Determine the third derivative of y = (x² – 1) (2x³ ...

A:

Q: 1.. The differential equation (3x² + 2.xy + 4y²)

A:

Q: 2 Find pxV 1+ 3x² dr, where P is the ellipse parametrized as follows: r(t) = , 0<t< 2n

A:

Q: Find the general term of the sequence, starting with n = 1. Determine whether the sequence converges...

A: leta1=2-8=1+1-1+7a2=3-9=2+1-2+7

Q: 3.b) Eliminate the Ar bitrary Constants in the equation B.a) Eliminate the Arbitrary Conatanta in th...

A: Using differential equations. To eliminate arbitrary constant 1.differentiate given equation as many...

Q: dy - y – 5a* – 3x? + 2x = 0 dx - 2y = 5x + 6x2 – 4x ln a + cx 5y = 2x + 4x? – 6x ln a + cæ %3D Optio...

A:

Q: III DISCUSS THE PROPERTIES OF THE CURVE AND SKETCH FULLY (drawn to scale) 1. y = (1/3)x - (1/2)x? - ...

A:

Q: Between 2006 and 2016, the number of applications for patents, N, grew by about 4.9% per year. That ...

A: Given: N'(t)=0.049 N(t)Therefore:dNdt=0.049 N

Q: 1 2) Evaluate n(n + 1)(n + 2) n=1 A B + n + 1 1 Hint: Find constants A, B and C such that п(п + 1)(п...

A: We are asked evaluate the given

Q: ædy – ydæ = (x² – y²)dy (tan y – 2)dæ + (* sec² y + +) dy =

A:

Q: A function f is given, and the indicated transformations are applied to its graph (in the given orde...

A: Topic:- function and its transformation   

Q: of

A:

Q: ſe^(3-z) sin(2+z) dz *

A:

Q: Q2) Solve given differential equation using undetermined coefficient superposition approach y" - 2y"...

A:

Q: A POPULATION OF INSECTS GROWS THERE Wtrt 170 INECTS AFTER THE THIRD DAY EXPONENTIALLY. OF THE EXPERI...

A: Find your answer below 

Q: 1. The differential equation x(3.xy – 4y' +6kdx+(x' – 6x²y² - 1\dy = 0 is exact because ƏM ƏN dy

A:

Q: Find x²z ds, where C is the line segment from (0,6,4) to (1,3,-2) C

A:   ∫C y ds,  C: x=t2, y=t,  -2≤t≤3   dxdt = 2t,   dydt= 1∫Cy ds = ∫-23 t  (2t)2+1 dt=∫-23 t  4t2+1 dt...

Q: For the given p-series, identify p and determine whether the series converges. 8. 2k413 k=1 p = .The...

A:

Q: Given the points A(-1,1,5) and B(2,5,0): a.) Find AB. b.) Find the equation of the sphere which has ...

A:

Q: dy y - 5a- da 3x2 + 2x = 0 %3D 2y = 5x + 6z² - 4x In a + cr 5y = 2a + 4x-6z In a+ ca %3D Option 1 O ...

A:

Q: 5. The differential equation (3r'e -21}dr +(r'e' -sin y Jdy = 0 is exact because ƏN %3D

A: Given:- Differential equation (3x2-2x) dx+(x3ey-siny)dy=0 To Find:- The given D.E is Exact because ∂...

Q: singx 4. lim x-0 sinnx

A:

Q: Eliminate Arbitrary Constant y^3(x+2y)=C^2y

A:

Q: Evaluate the following functions. 1. lim x2 • coS X X 4.

A: Our Aim is to evaluate the function given below:-limx→π4x2. cos (x) -(i)

Q: y = C1e¬ª + C2e¯2# + x y" + 3y – 2x + 2y – 3 = 0 y" – 3y – 2x – 2y+ 3 = 0 - - Option 1 Option 3 y" –...

A:

Q: Determine C when x=y=0 (xy+ 2)dx = (x'y +x² + y? + (z²y + z? + y} +1) dy %3D

A:

Q: What is the particular solution if y(1)=D0? 1/2 xy = y+ (a² + y³)2

A:

Q: dy Find in simplest form in each of the following dx - 5 1. y = - x³ – 4x² + 7x – 5 in

A: Given that: y=-5x3-4x2+7x-5     NOTE: As per our answering guidelines, we can only answer 1 question...

Q: Find the value of 6dx x2 + 1

A: Use simple integrations concept. 

Q: Find two positive numbers whose product is 36 and whose sum is a minimum. (If both values are the sa...

A:

Q: d.f* .3 e x* dx

A: The given improper integral is: ∫0∞ e-x3 dx

Q: Let {xn} be a bounded sequence on R. Show that Xn lim = 0. - n→+∞ n

A: follow next step

Q: A Norman window has the shape of a rectangle surmounted by a semicircle. (Thus the diameter of the s...

A:

Q: The expression ā o (b o č) represents O a scalar something that does not make sense O a vector O a l...

A: I am attaching image so that you understand each and every step.

Q: Find unit vector in the direction of . Show all your work on your own paper; leave the box below BLA...

A: We are asked to find the unit vector in the direction.

Q: Use the properties of logarithms to expand the expression as a sum, difference, and/or constant mult...

A:

Q: = 1. Find the general term of the sequence, starting with n = Determine whether the sequence converg...

A:

Q: (3x*y + 4.xy' + 6)dx + (r* +6r°y -1}ty = 0 1.

A:

Q: dy Find dx if y = cos e*

A:

Q: Find the limit. Use l'Hospital's Rule where appropriate. If there is a more elementary method, consi...

A:

Q: dy sin x Find in y = dx 1+ cos x 2 2 2 cosʻ x+ sin´ x+cos x cosʻ x+ sin´x а. b. (1+ cos x) (1+ cos x...

A: Topic :- derivatives 

Q: Find each of the two areas bounded by the curves y = x3 - 4x and y = x2 + 2x

A: The graph is shown below: