1. Two particles travel along the space curves r, (t) = (t, t,t) and r2 (t) = (1+ 2t, 1+ 6t, 1+ 14t), do their paths intersect? Do the particles collide? If so, determine the point(s) of intersection.

Q: 1 The 2nd degree Taylor polynomial for the function f(x) = In x, xo = 3 is P2(x) = In(3) + ÷(x– 3) +...

A:

Q: sec (0) J de 5-sec2(0)

A:

Q: et sin x – x lim x → 0 3 cos x – 3 - (Us

A: Given: limx→0exsinx-x3cosx-3   We know that; The Product rule: f·g'=f'·g+f·g'

Q: 18. What is the integrating factor of the differential equation y' =cscx-ycotx ? a. tan x C. sinx b....

A: This is a question related to differential equation. Based on the formula of integrating factor we w...

Q: Question 12 Evaluate: J(7x3 + 4x²2)dx 7x4 4x2 +C 2 A 4 (B) None of the given choices 7x4. 4x3 + C 3 ...

A: The given integral,        ∫7x3+4x2dx

Q: Activity 2: Determine the equations of the normal at each of the points indicated 1. f(x) = x² + 3x ...

A:

Q: 12 ("In xdx 5 a) Find the smallest K such that | f4) (x)| <K for 5 <x< 12. b) Use the part (a) answe...

A: Let's find. 

Q: A large tank filled with 500 gallons of pure water. Brine containing 2 pounds of salt per gallon i...

A: Let A(t) is pounds of salt in the tank at time t.We know that dAdt=Rin-Rout

Q: he integrating factor to the linear differential equation x(x² +1)y' +2y = (x² +1)° is:

A:

Q: Solve for the particular solution yp of the given differential equation: y" + 3y' + 4y = 4x2 — 2х -

A: Given differential equation, y''+3y'+4y=4x2-2x⇒(D2+3D+4)y=4x2-2x          D≡ddx.............(i)

Q: Is this function analytic fizz=. (1 +x)? +y2 2

A:

Q: Determine whether the series converges. 00 1 Σ k+19 k=1 The series eTextbo diverges converges

A: ∑1∞ 1/(k+19) =∫1∞ 1/(k+19) =ln(k+19)]1∞ =∞ - 0 =∞ so the series is diverges to ∞

Q: Find

A: We will solve find the anti derivative or integration. 

Q: diverges. Ifit conveges, find the Determine whethe the seauence converges or 3n an=

A:

Q: Complete the following statements by entering numerical values into the input boxes. Angles are meas...

A:

Q: Evaluate the derivative of the function at the given point. 1 t = 3 8t + 1 y =

A:

Q: S(tan e" +sece" }'e= de

A: follow next step

Q: 5. Find the volume of the solids generated by revolving the regions bounded by the curve y = secx, -...

A: To find out the volume of revolution. 

Q: b. Consider the function g(x) = 2.8 sin(3r) i. What is the period of g? radians Preview ii. What is ...

A: Given query is to find period amplitude and the midline of the sine function.

Q: 9. What is the solution of (x? + 2xy – 4y² )dx – (x² – 8xy – 4y² )dy =0 ? a. x? - 4y? = c(x-y) b. x?...

A: This is homogeneous differential equation. For solving this we will assume,  Y/X = V dy/dx = v - xdv...

Q: f(z+h)-f(x) For f(r) V7z 1 37, findf (z) using the definition f '(z) = lim h30 h "(z) sing this, fin...

A: Given query is to find derivative by definition and equation of tangent.

Q: A parabola having its x axis parallel to the y-axis has its focus at (5,6) and vertex at (5,4). Comp...

A:

Q: For all of the following questions, assume is in radians. a. Consider the function f(x) = sin(x). i....

A: Topic:- function

Q: consider the polynomial equation P(x)=x^5 + 3x^4-25x^3-79x^2+100=0. Use synthetic division to determ...

A:

Q: 8.Expand the function F(x) =e ^3x-1 by using the Taylor order 4 polynomial, then approximate the val...

A:

Q: Evaluate. Show all your worH In x -dp- 1 5

A: Here, to evalaute the defiite integral: I=∫5∞ln xx2dx...(1)

Q: Classify the series as absolutely convergent, conditionally convergent, or divergent. (– 1)k+1 Σ 5k ...

A: Please refer to the image below

Q: Determine whether the alternating series converges. k + 1 | 10k + 1 k=1 O The series converges. O Th...

A: In this question we have to find whether the series is convergent or not.

Q: Evaluate the integral given below. Check your answer by differentiating. NOTE: Enter the exact answe...

A:

Q: Determine whether the series converges, and if so find its sum. 4k+2 Σ 7メー1 k=1

A:

Q: using the substitution u = cos(x). cos (x) sin(x) dx = +C

A: Topic:- integration

Q: Find the solution of the given initial value problem. 8. cos t y(T) = 0, t>0 %3D t8 y(t) = %3D

A:

Q: Solve the logarithmic equation for x : log2 (x - 2) + log2 (x - 3) = 1

A:

Q: c In Problems 53-74, summarize the pertinent information obtainea by applying the graphing strategy ...

A:

Q: Use the difference an+1 – an to show that the sequence {n – 2"}n=1 +o0 is strictly increasing or str...

A:

Q: 7. One secretary can do a particular job in 6 hours and another secretary can do the same job in 4 h...

A: Topic:- algebra  Note:- as per our guideline if more than one question uploaded than only first ques...

Q: The following situation applies to the attached question The fluid pressure (in atmospheres) at the ...

A: Px,y = 1+ x2y10Where, P : Fluid pressure in atmosphere at the bottom of a body of liquid of       va...

Q: Question 2 ( sin (x) + sin(x) cos²(x) To evaluate the -dx using basic formula of integration (withou...

A: Topic  -  integration Ans   1.496 

Q: Problem 3. Use the method of Lagrange multipliers to find the indicated еxtremum. You may assuтe the...

A:

Q: Determine whether the series converges. 1 Σ k + 20 k=1 The series >

A: We are asked to  find the series is convergence or divergence.

Q: (у? + ту?) da + (5у? — ту + у' sin у) dy 3D 0 Let M be the coefficient of dx and N be the coefficien...

A:

Q: a. Find the derivative function f' for the function f. b. Find an equation of the line tangent to th...

A:

Q: Evaluate the integral. Show all your work. 3 (sec' xdx

A:

Q: e dx PROBLEM 2: J 5e -4 2 csc" wdw cSC PROBLEM 3 : 1+cot w

A:

Q: Iculate the derivative indicated. d'y 1 + 322 where y = da2 \1 7 23 nswer:

A: d/dx(x^n) = x^(n+1)/(n+1)

Q: Find a differential equation that corresponds to the given direction field. Consider differential eq...

A: From The Direction Field : Slope Field at y = 3 is Parallel to t - axis So, Slope at y = 3 is 0. so,...

Q: Find the solution of the given initial value problem in explicit form. 1 y/ = (1 – 5x)y² , y(0) %3D ...

A:

Q: +0 An+1 -to determine if the sequence An n Use the ratio is strictly increasing or strictly 2n + 2 J...

A: Topic:- sequence and series

Q: For the next five questions, consider the following differential equation: (y? + cy°)dx + (5y² – xy+...

A: Given differential equation is y2+xy3 dx + ( 5y2-xy+y3siny) dy =0 Also, given that M is coefficient ...

Q: 14. For the function f (x) = 10 - 5x find the average rate of change from x = a to x = a + h %3D

A: