Consider the vector function r(t) = (t, t,t¹) Compute r' (t) = ( T(1) = ( r" (t) = ( r' (t) x r" (t) = (

Q: #1 #2 2/2J (8 + 4 cos x) dx •3 [² - 10 (1 − e¯x) dx

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Q: cos² (x) y' = y + tan x

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Q: The curves →r1(t)=⟨5t,t5,4t4⟩ and →r2(t)=⟨sin(5t),sin(t),t⟩ intersect at the origin. Find the acute…

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Q: Sketch the region enclosed by the given curves. Decide whe graph.) y = |x|, y = x² − 6 Then find the…

A: The region S is bounded by the curves y=x, y=x2-6 We have to sketch the graph of the region and find…

Q: 3) -) :) [-1, 8] minimum maximum (4,9] minimum maximum (0,8) minimum maximum [4, 10) minimum maximum…

A: We will find the required.

Q: A child enters a carousel that takes one minute to revolve once around. The child enters at the…

A: Concept: Starting from the point (0,1) a child circles around counterclockwise If it takes 1minute…

Q: f(x) = x +2+1 202

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Q: 'x -S² f(t) dt, where f is the function whose graph is shown. _et g(x) = y 1 0 1 3 f 6 9 t i

A: Given graph:-

Q: 2. Find the solution of the given initial value problem. y" - 6y +9y = 0, y(0) = 1, y'(0) = 2.

A: Giveny'' -6y' +9y=0

Q: lim x->4 4 1 √x-2 x-4

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Q: dy dx For the equation +7x²y = 0, y(0) ==, the value of y(1) is 3,

A: Given :dydx+7x2y=0

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

A: We need to find  out the volume of revolution for the given function on the interval given.

Q: Consider the following function. 1 f(x) = x² - 3 Determine whether f(x) approaches ∞ or -∞ as x…

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Q: ider the following. f(x) = 1 x+2 (a) State the domain of the function. all real numbers x all real…

A: Given query is to find characteristics of the function.

Q: An aquarium 6 ft long, 3 ft wide, and 2 ft deep is full of water. (Recall that the weight density of…

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Q: If tant - 5 12 and π < t < 3π 2 find sint, cost, sect, csct, cott.

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Q: Given the following functions, compute the composition (fog)(x). f(x) = 2x+8 g(x) = 3x - 6 Simplify…

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Q: 3. Find the function that is finally graphed after the following transformations are applied to the…

A: Given curvef(x)=x

Q: II. Determine the point(s) of intersection, m, and m,, and the angle(s) of intersection of the given…

A: Disclaimer:  “Since you have asked multiple question, we will solve the first question for you. If…

Q: Question 6. Find an equation for the surface consisting of all points P that are equidistant from…

A: See this solution in below.

Q: Tutorial Exercise Find the volume V of the solid obtained by rotating the region bounded by the…

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Q: A B The integrating factor for (2y - xy2)dx − (3x+x²y)dy = 0 is 5 2xy 1 5xy .. ..

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Q: Find the partial fraction decomposition of -6x - 16 x² + 6x + 8

A: -6x-16x2+6x+8

Q: Determine the curvature of the elliptic helix r = : (7 cos (t), 8 sin (t), 8t) at the point when t =…

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Q: domain is all real numbers. global maximum at t = global minimum at t = (Enter none if there is no…

A: Topic:- application of derivatives

Q: In Exercises the region. 35. 8 6 4+ 2 2 ++ use an iterated integral to find the area of (8,3) 4 6 8

A: As we know the Power rule: ∫xndx=xn+1n+1+C ; where n≠-1   The given bounded region is: Use the…

Q: Let r(t) = (2 cos²t, 2 sin²t, 2t), find the exact value of the curvature of r(t) at the point 31 π…

A: This question can be solved using the concept of radius of curvature.Radius of…

Q: 2 2. Is f(x) = { = { x²-1 x+1 if x = -1 if x −1 continuous at x = −1? (Show your work using limits.)

A: See this solution in below.

Q: AI P A2 a) Find P & Q b) Find the areas of P₁ & A2 y=sinx y=sin2x

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Q: 5c

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Q: 2. Given the following information, calculate the equation of the tangent line to f(x) at x = a: a=0…

A: Equation of tangent line at point a=0

Q: Solution of the differential equation y cos²x dz y cos5 x ytanx - sinzcos² T y² cos²x = sinºz + c…

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Q: Find the following derivative and state a corresponding integration formula. 3x - 1 2x2 + 2x + 2 d…

A: Derivative

Q: Evaluate the following integral by interpreting it in 3 1₁ (2 - x) dx =

A: Graph of  | x | graph of - | x | is reflection of | x | about x axis  graph of 2 - | x | is…

Q: Determine the following limit. lim 6x18 8118 18 lim 6x 8118 =

A: Here we have to find the limit.

Q: lim -3x7 + 7x³ – 5. X→∞

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Q: The surface area S of a sphere of radius r is given by S(r) = 4². Explain why, in the given context,…

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Q: dT Consider the differential equation x +T=e* with 7(0) = 1. What is the approximate value dx of…

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Q: In Exercises , sketch the region R of integration and switch the order of integration. 47. f. f.…

A: According to bartleby guidelines when student post more than one question then expert must have to…

Q: dy dx 3 For the equation +7x²y = 0, y(0) = 2, the value of y(1) is

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Q: p(x) q(x) points for such a function? 1. Suppose f'(x) = where p(x) is linear and q (x) is a…

A: A point x=a is said to be a critical point of a function f(x) if(i) f(a) exists  and (ii) f'(a)=0…

Q: Use the properties of the derivative to find the following. r(t) = ti + 4tj + t²k, u(t) = 5ti + t²j…

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Q: The left, right, trapezoidal, and midpoint rule approximations were used to estimate =1²₁ f(x) dx,…

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Q: The strength of a patient's reaction to a dose of x milligrams of a certain drug is R(x) = 8x√16…

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Q: =1+²+ + 3x + 9 Find the critical numbers. (Enter your answers as a comma-separated list. If an…

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Q: DO THIS TYPEWRITTEN FOR UPVOTE

A: We need to find out the slope of the tangent line and normal line and their equations which passes…

Q: dx 2. Evaluate the improper integral Sª Why is it an improper integral? (x - 1)² 3. Find the arc…

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Q: A B Which of the following is an integrating factor for ydx-xdy = 0 ? X

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Q: Evaluate S² (ti + t²j + t³k)dt = i+ j+ k.

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Q: dx 2. Evaluate the improper integral S Why is it an improper integral? (x − 1)² 3. Find the arc…

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