Find the limit. Use l'Hospital's Rule where appropriate ex + e-X - 2 lim x-0 ex – x – 1

Q: 4. f(r, y) = + y + xy,find fay and fyz

A: Solve the following

Q: wnd the point of intersection of the line through (1, -3, 1) and (3, -10, 5), and the plane given by...

A:

Q: 1. sinx siny dx + cosx cosy dy = 0 %3D 2. [2xy cos(x2) – 2xy + 1]dx + [sin(x²) – x²]dy = 0 3. y?dx +...

A:

Q: y = cos(2x), y = sin x, 0<x< 2

A: Solution is given below:

Q: 1. Evaluate the integral: SSf, xe**+y<+zt dV where B is the portion of the unit ball x² + y² + z² < ...

A: Here, the region B is the portion of the unit ball x2+y2+z2≤1 that lies in the first octant. Convert...

Q: Solve the following problems. Show complete solutions. 1. S sin° (2æ) cos (2æ)dæ

A:

Q: 1. Use the Root Test to determine if the series en? n=1 (-1)"2* (2n2 – 1)n converges or diverges.

A:

Q: Find the area of the parallelogram that has u =i – 2j + k and v = 3j +k as adjacent sides. NOTE: Ent...

A:

Q: Solve the following equation using bisection method to find the root between x1=1 and x2=3 make 5 it...

A: Given,f(x)=3x3-10x-14We want to find root of function between 1 and 3Thereforef(1)=3(1)3-10(1)-14f(1...

Q: 1. Let f(x) = 1 – x2/3. Show that f(1) = f(-1). This means that by Rolle's the- orem there should be...

A:

Q: Sketch the region R of integration and switch the order of integration. f(x, y) dx dy 8 6 6 y 4- y 4...

A: This is a problem of integration. Based on the x and y limit we will sketch the region. 

Q: 10. Find. the Valume.f. the Salid.baundeel.by. the.cylinder. X=y and. the.planes.Zz. and.x+2=.. Ans....

A:

Q: 1 S cos³ 3x sin' 3x dx

A: The given integral is: I=∫cos33xsin43xdx   ...1   We know that; The Power rule: ∫xndx=xn+1n+1+C

Q: Find the derivative of the function at Po in the direction of u. f(x, y, z) = In(x 2 + 3y 2 + 9z 2),...

A: Since you have posted multiple questions i can do first question as per our company guidelines pleas...

Q: 1. Using the Root Test, determine whether the series (-1)"en: sin 2n '(금) is absolutely convergent, ...

A: This is a problem of series and sum calculator. Based on the general formula of series we will answe...

Q: Consider the points A(3, –3, 3), B(4, –5,0), C(-3, –4, 0), and D(6, 2, –6). (a) Find the volume of t...

A: We have to find the volume and distance of given question 

Q: (a) Oppositely directed to v = (9, – 18) and half the length of v. w =|(?,?) (b) Length 5 and same d...

A:

Q: Find two vectors in opposite directions that are orthogonal to the vector u. (The answers are not un...

A: To find: The vectors in the opposite direction that are orthogonal to the vector u Given information...

Q: Sketch the region bounded by the given curves, then find its area. 1. у%3D х*, у%3D2х

A: Since the student has posted multiple questions and does not mention any specific question, so we ar...

Q: Find the absolute maximum and absolute minimum values of f on the given interval. f(x) = 17 + 4x - x...

A: Given function f(x)=17+4x-x2   ; [0,5]

Q: 3. 2x y' = y(3x*+y?)

A: We need to solve the differential equation by integrating factor.   NOTE - As per Bartleby's guideli...

Q: 1. lim 3 2. lim 57 3. lim log r

A:

Q: 6. On a certain workday, the rate, in tons per hour, at which unprocessed gravel arrives at a gravel...

A: 6) Given that the rate in tons per hour at which unprocessed gravel arrives at a gravel processing p...

Q: 1 )dx 4.

A: We will use substitution method to solve question 4.

Q: The function y = 2x2 for -3 ≤ x ≤ 3 is given. a) Plot the graph b) Find the gradient at x = 1

A:

Q: 2xy cos(x^2) - 2xy + 1]dx + [sin (x^2) - x^2]dy = 0

A: Note : “Since you have asked multiple question, we will solve the first question for you. To get rem...

Q: Find the solution of the following Differential Equations 8) y-2y'+2y = 2e" cos(x)

A: The given DE is: y''-2y'+2y=2excos(x) Now, the homogeneous form of the given DE is: y''-2y'+2y=0 The...

Q: ne unknown initial temperature, 3. If the temperature of the air is 300K and the substance cools fro...

A: As per the guidelines I can solve only first question 

Q: Voter Registration The amount of voters in a city's district should grow at the rate of 1500 / (8 ...

A: at present it is = 25000 after 2.5 year so t =2.5 growth = 1500/(8 + (2.5)2 )0.5  growth = 1500/(8+6...

Q: Pls solve using Integrating Factors Found by Formulas: xydx - (x^2 + 2y^2)dy = 0

A:

Q: Question 15 Write a chain rule formula for the following derivative. for w = f(x, y, z); x = g(s, t)...

A:

Q: Sketch the region R of integration and switch the order of integration. 36 - x fx, у) dy dx y

A: Given problem:-

Q: s. Evalnate.the following.deuble.integrals.by.converting.bo polar.Coa.r.dinates. C.. Ans: 3.6.

A:

Q: Pls help ASAP. Pls show all work and calculations

A:

Q: S sinxcos(2x)dx

A: We need to evaluate the following integral I = ∫sinxcos2xdx Formula Used: ∫xndx = xn+1n+1+C

Q: n. 2n + 1 Σ n tan -1 n n=1

A:

Q: Consider the following planes. 5x + 2y - z = 44 X - 4y + 2z = 0 (a) Find the angle between the two p...

A:

Q: Consider the following. u = -9i – 4j – 2k, v = 4j + 4k (a) Find the projection of u onto v. (b) Find...

A:

Q: 2 y = 12 – 3x", y= 4 – x- — х |

A: Let's find. 

Q: ハメー X1 YxJ dx |

A: Find the integral

Q: Consider the sequence c= {3, –12, 48, – 192, 768, ..} - | a. What is the common ratio? b. What are t...

A:

Q: 9. 10 Find the rate at which average revenue is changing when An accessories company finds that the ...

A:

Q: find the area of the Shaded Part AUsing Polar y =2X

A:

Q: 11. If x is a right endpoint and f'(x) is positive on the interval to the left of x, then f(x) has a...

A: Given

Q: An object is released from rest, at a height of 1250 feet above the ground. The height of the object...

A:

Q: (2у — Зx)dx + xdy 3D 0

A:

Q: Find an equation for the plane through points P(1, -1,2), Q(2,1,3) and R(-1,2,–1).

A: This question can be solved by applying the formula of equation of plane passing through three non c...

Q: Write the equation of a parabola whose directrix is y = - 0.75 and has a focus at (– 8, 8.75).

A: Let's find. 

Q: 1 de, where a, b, and d are real and a² + b² < d² a cos e + bsin 0+d

A: The given integral is: ∫02π1acosθ+bsinθ+ddθ Also given that: a2+b2&lt;d2.

Q: Let F and G be vector-valued functions such that F(t) = (cos(nt), e²t-1, t² – 1), Ġ(1) = (1, 1, – 1)...

A: