Find the length of one turn of the helix given by r(t) == cos(t)i + sin(t)j + 1 1 99 25 -tk.

Q: 2 1 Expand 2y 0.013 2 3. ✓0.0004:

A: Given problem:- Expand 2y210.013y2230.0004

Q: Consider y=√x+1. (a) Find its inverse relation. Is this relation a function? Why? If the inverse is…

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Q: What are the associated roots forR (x) in the differential equationy''- y = R(x) where R(x) = 4cosx?…

A: Given differential equation:- y"-y = R(x) Where R(x) = 4 cosx

Q: = Farmer Jones, and his wife, Dr. Jones, decide to build a fence in their field, to keep the sheep…

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Q: Set up the definite integral required to find the area of the region between the graph of y = 17 -…

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Q: a. Find the linear approximating polynomial for the following function centered at the given point…

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Q: f(x, y, z) = 2 ≤ x ≤ 10,0 ≤ y ≤ 4,0 ≤ z ≤4

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Q: What is the general solution to the the differential equation 3y''-y' - 2y=0? (2/2)

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Q: 6. a) State why the limit of f(x) = √5x - 1 does not exist for x

A: Please refer to the image below

Q: Find (3x + y)dA where D = {(x, y) | x² + y² ≤ 16, z ≥ 0} Round your answer to four decimal places.

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Q: Given the function f(x)= |x-1|: (a) explain why f(x)= |x-1| does not have an inverse function over…

A: Given fx=x-1

Q: Determine the infinite limit: O -∞ O 8 7-x lim x 4 x² - 2x - 8

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Q: Solve: xy + y + 4x³y¹ = 0 O 6ry³ + Cr³y³ = 1 O 15r y³ +Cr³y³ = 4 O9r³y³ + Cr³y³ = 5 O 2r³y³ + Cr³y³…

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Q: 5₂00⁰ dx 2 3 1.

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Q: a. Find the linear approximating polynomial for the following function centered at the given point…

A: Given f(x)=1xa=1

Q: b) 2 1/2 dx x(lnx)4

A: Topic:- integration

Q: 1 6. √₁² √ 1 - √u du

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Q: A microwaveable cup-of-soup package needs to be constructed in the shape of cylinder to hold 600…

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Q: A diabetes test is positive 85% of the time when the patient has diabetes and negative 95% of the…

A: Given data:- Diabetes test is positive 85% of the time when the patient has diabetes  diabetes test…

Q: Use polar coordinates to evaluate the double integral. 1 1 + x² + y² where R is the sector in the…

A: Given data:- the double integral, ∫∫R11+x2+y2 dA R is the region y=0, y=x, and  x2+y2=4

Q: 1. Which of the following functions grows the fastest as x goes to infinity? O 2x О 3x O Ox20 ex

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Q: Find the sum by adding each term together. Use the summation capabilities of a graphing utility to…

A: We have to find the sum  ∑j=16 8j + 5.

Q: 0 4 From a square piece of metal of side length 6 m, four squares are removed as shown in the…

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Q: Let à = (1, -2, 0) and 6 = (1, 3,2). b Find the angle between the vector (in radians) Check Answer

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Q: Evaluate the limit of the given functions. 3x² - 17x+ 20 25x + 36 1. 2. lim x+44x² t³-1 1 lim t-1…

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Q: 9. Find the area bounded by a parabola and any right chord. (Use the parabola y² ax, chord x = x1.)

A: solution is given below..

Q: Find the acceleration vector for the position vector r(t) = (sin(11t), 4tº, e -2t). x component = y…

A: We need to find acceleration vector.

Q: Problem Set question: The position function for a falling objects is given by s (t) = -16t² + vot +…

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Q: Let v = 17 + 17 and w = 17 + 8j. Find a number c so that w- cv is perpendicular to v. C =

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Q: Consider the set A = {1/2^{n-1}: n\epsilon \mathbb{N}}. Show that Inf(A) = 0. WITHOUT USING LIMITS

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Q: 2. cotx = sin xsin π 2 --x+cos² x cotx

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Q: Let the position function of a particle be r = (t, t², 0). Find the normal component of the…

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Q: You are taking a road trip in a car without A/C. The temperture in the car is 105 degrees F. You buy…

A: Above question is solved.

Q: e) 9x³ + 6x² + 18x + 12

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Q: Find the generated volume f(x)=sin(x) and the lines x=0 and x=π and rotate about the x-axis V=π^2…

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Q: Find SS₁² 6x d.A over the region R = {(x, y) | 0≤x≤ 2,0 ≤ y ≤ 5} by identifying it as the volume of…

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Q: 2 Let F(t) = (+²5¹ √5t – 2, sin (5t)). t-5' fF(t)dt f(t)dt = ([ Find (don't include the +C) + C

A: Above question is solved.

Q: 3. A ladder 10 feet long is leaning against the wall of a house. The base of the ladder is pulled…

A: Concept: Let x represent the distance from the wall to the ladder's base. and let y be the height of…

Q: Sketch the region enclosed by y = 7x and y = 9x². Find the area of the region.

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Q: 1. Find the volume of the solid that results when the shaded region is revolved about the indicated…

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Q: 4. 5⁰ -x² xe dx

A: Given Problem:- ∫0∞xe-x2dx

Q: f(x) 3. What does lim = 0 show? X→∞ g(x) O g(x) grows faster than f(x) as x goes to infinity. Of(x)…

A: The given limit is limx→∞fxgx=0

Q: Solve the differential equation -1 (x + 3)¯¹ cos (y)dx cos (y)dx O a. cos (y) In b. cos (y) In -…

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Q: Solve the differential equation (1 − xy)−²dx + [y² + x²(1 — xy)−²] dy + x²(1 − xy)−²] dy = 0; y (2)…

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Q: The cross product is anti-commutative. This means that axb=-bxa. Show this is true for a=(2,3,4), b…

A: Given  a→=2,3,4 and b→=-5,-4,-3. We have to show that  a→×b→ = -b→×a→.

Q: √√√x- S: z 12, x² + y² ≤ 1 Evaluate (x - 2y + z) ds.

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Q: 1. Evaluate the following matrix operation: [5 3 a. A = 1 -4-3-1 L2 b. |B| C. C = 31-33+231 5+20 0 1…

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Q: 6. x³-x²-x+10 lim x-2 x² + 3x + 2

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Q: Which function has Maclaurin series (-1)"2""? n:o OAI OB 8. 2/7/2 Oc O D. TIZE D.E. 2

A: The given series: ∑n=0∞-1n2nxn

Q: Find Ž k=0 the convergence Set for each

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