Evaluate the following limit: x + 2 lim x→-3¯ x² -+ 2x – 3 O +∞ 10

Q: Find the vector v with the given magnitude and the same direction as u. Magnitude Direction ||v|| =…

A:

Q: If the amount of bacteria in a culture at any time increases at a rate proportional to the amount of…

A: answer is in next step

Q: Using Euler's Method, approximate the initial value problem for various values of x given in the…

A:

Q: What is the area of the region bounded by the graph of r = 4 cos 20? Choose two (2) correct answers.…

A: Let's find.

Q: Use the Direct Comparison Test to determine the convergence or divergence of the series. 00 sin“(n)…

A: We have to find the convergence of series

Q: The sales function for a product is given by S(x) 124 + 37.8x? – 0.6x, wherex represents thousands…

A:

Q: Find the area of the region enclosed between the curves defined by the equations y = vx +2,y= x ,…

A:

Q: Suppose that the number of employees in a new company is expected to grow, with the number of…

A:

Q: 2. Show that if x and y are two vectors, then

A: Replace x→ by u→ & y→ by v→     Graphing software do not accept label x, y To show: u - v ≤u±v≤u…

Q: 2 Integrate | 20(5æ – 3)°dæ - – 2

A:

Q: 11. Use the guideline in §4.4 to sketch the curve: f(x) = x² ln x. A). Domain, Symmetry, Asymptotes,…

A:

Q: Find a plane through the points (-3,-1,-8), (-2,4,-7), (1,6,-4)

A:

Q: The slope of the tangent line is

A:

Q: Laplace transform of (t+2)^2

A:

Q: A lighted candie burns outr according to the equation y'(1) =ky (1) where y is the length (in…

A: see below the answer and explanation

Q: Find the equation of the tangent line to the graph of y = -2x° + 6x? – 5x + 10 at the point (1,5) in…

A:

Q: Which type of discontinuity does the function S4- a², In x, x < 1 f(x) = 1<x < e has at x 1?

A: We need to choose correct option.

Q: Find y': y = /5+ 2x – x² - 1-x O y = V5+2x-a2 1 O y = 2/5+2x-a2 7-2x O y = 2/5+2x-a²2 O y = /2 – 2x

A:

Q: The surface S is parametrized by equations x = u + v, y = 3u?, z = u – v; The point P (2, 3, 0) lies…

A:

Q: Find V x (V x F) if F(x, y, z) = 2xy j+ 6xyz k. %3D V × (V × F) =

A:

Q: Find the average value of y = sin x between x = 0 to x = π.

A:

Q: ||r'(t) × r"(t)|| ||r"(t)||* Use the formula k(t) = to find k(t). r(t) = t²i + t°j %3D K(t) =

A: Given: r(t) = t2i +t5j Solution: r'(t) =ddtt2i+t5j =2t i +5t4j r"(t) =ddt2t i +5t4j= 2i + 20t3j

Q: Find div F and curl F if F(x, y, z) = 3y°z°i – 3x*2°j – 3xy*k. - div F= curl F=

A:

Q: Find the position vector for a particle with acceleration, initial velocity, and initial position…

A:

Q: 1 2 3 1+3* Use substitution to find the Taylor series at x= 0 of the function ... 1 What is the…

A:

Q: d²y of the following equation then simplify whenever possible. 3) Find and dx dx- x = 3em y = 4e-m

A:

Q: Find T(t) and N(t) at the given point. r(t) = 11 cos(t)i + 11 sin(t)j + tk; t= -11 /122 T(5) V122 0,…

A: Given: r(t)=11cos(t)i→+11sin(t)j→+tk→ r'(t)=d11cos(t)dti→+d11sin(t)dtj→+dtdtk→…

Q: Given the function f(x) = x2 and the closed interval [0, 1, which of the following is a value of c…

A:

Q: A man 6 ft tall is walking toward a building at the rate of 5 ft/s. There is a light on the ground…

A:

Q: Find a particular solution of the DE: y" – 6y' + 8y = 64x?. C. yp = 8x + 12x + 7 E. None A. Yp = 4x?…

A: Solve it

Q: 1 dx Vx - Vx 3

A:

Q: Kuya Bill is selling 'Bill phones'. If the cost for selling r phones is given by 10000 C(r) = 120x +…

A: Given, Cost function, C(x) = 120x + 10000/x - 2000 Price Dand function, p(x) = 1000 - 2000/x2 + 200x

Q: Consider the following planes. -6x + y + z = 6 18x - 3y + 6z = 36 (a) Find the angle between the two…

A:

Q: Find div F and curl F if F(x,y, z) = x°i – 5j + yzk. - div F= curl F=

A: A detailed solution is given below

Q: 2. Let f(x) = vVI(2 – x). Use the local linear approximation of f(x) at xo V0.99 (1.01)². 1 to…

A: Explained below

Q: Evaluate F. dr. Jc F(x, y) = 7xi + 8yj C: r(t) = ti + v4 - tj, -2 st s 2

A:

Q: Evaluate the derivative of the function: x2 f(x) = ( x²+1 8x (æ²+1)° O 8a(a² –1) (2²+1) O 1 4x…

A: Use the chain rule for finding the derivative

Q: For the function g whose graph is given, state the following. (If the answer is positive infinite,…

A: As per our guidelines we are supposed to answer only first three parts. Kindly repost others…

Q: Find curl(4= i+ 5x j+ 6y k). curl(4: i+ 5x j + 6y k) = ( i )i + ( i )j +( i

A: We have to find curl

Q: Find ke ende finite integral. cuse c for Ge Constant of entyration) J Sin 39 Jcos 34 de (the + are…

A: We need to solve integral.

Q: Let S1 be the hemisphere with Cartesian equation z = 6 – /36 – x² – y? and S2 be the upper nappe of…

A:

Q: D If the Taylor series expansion for f (x) is given by f(x) = Eo- (x- 2)*, then f(4) (2) = %3D

A:

Q: t"(x) If t(x) = Vx find t'(x)' O -1/2x O 2x 1/2x -2x O None of these

A:

Q: Use Stokes' Theorem to evaluate curl F· ds. F(x, y, z) = ze'i + x cos(y)j + xz sin(y)k, S is the…

A: Stoke's theorem: The surface integral of the normal component of the curl of F is equal to the line…

Q: Let h(x)= f(g(x)) where f(x)=tanx. Then h'(x)= a) f'(tan x) g'(x) b) g'(x)tan(g(x)) c) g(x)…

A:

Q: Double USA, manufacture of the Nicolas cage pillow has determined that the marginal daily revenue…

A:

Q: О а. 1.56 J ОЬ. 3.25 J Ос. 1.94 J O d. 2.33 J

A:

Q: A 25-year old woman burns 350 Gatorade is 55t calories during the tth hour. What is her net decrease…

A: A 25‐year old woman burns 350-60t cal/hr while walking on her treadmill. Her caloric intake from…

Q: Evaluate: Lī 3sin13 xda 512 1001 1024 1001 1024 1001 512 1001

A: Solved below.

Q: Find V x (V × F) if F(x, y, z) = 5xyj+ 10xyz k. V × (V × F) =

A: