Consider the helix r(t) = (cos(1t), sin(1t), 4t). Compute, at = 7:

Q: Example 4. Determine the arc length of the curve r(t) = (2t, }(t — 5)³/², -t) between 1 < t <3.

A: we need to find the arc length of the given curve.Arc length, L=∫abr'tdt

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Q: Find E Only E) Find the profit function in terms of x

A: Given: R(x)=-0.001x2+4xC(x)=1162.80+1.21x

Q: Sketch the circle r = 10 sin 0. Give polar coordinates for its center and identify its radius. The…

A: Sketch:

Q: Find c such that the function - 6 x ≤ c f(x) 22 x > c is continuous everywhere. C = x² {3²2 8x

A: The function is given by fx = x2-6, x≤c8x-22, x&gt;c To evaluate: The value of c such that the…

Q: Solve the following linear differential equations. (a) (t²+1)y' - (2t+1)y=0

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Q: Consider the function below. Use it to find the following limits. (If an answer does not exist,…

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Q: Let R be the region inside the polar curve r = cos(0) and inside the polar curve r = 1 - sin(0), as…

A: Area bounded by curves

Q: Find the area of the parallelogram whose vertices are given below. A(0,0,0) B(4,3,5) C(6,1,5)…

A: To find the area of the parallelogram whose vertices are given below. A0, 0, 0, B4, 3, 5, C6, 1, 5,…

Q: If lim f(x) = 2.5 and lim f(x) exists, then what is the value of the limit where it exists? T→3 2-3…

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Q: Find an equation of the plane. The plane that passes through the point (-2, 3, 3) and contains the…

A: Given: Plane passes through point (-2, 3, 3) and it contains two lines x+y-z = 3 and 4x-y+5z = 2  To…

Q: Determine whether A and B are inverses by calculating AB and BA. Show all work. ∙1 A = · [²₁₁₂₁³₁] B…

A: To determine whether the given matrices A and B are inverses or not.

Q: 1. DETAILS Suppose you drive your car on a cold day and the engine overheats. When you park your…

A: The answer is in step 2.

Q: 3. Determine the following function f has a removable discontinuity at c. Rdefine f(c) so that f is…

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Q: Find the equation of the lime passes through (2,3) and // ar ] to the lan 2X-6Y=5 I

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

Q: Calculate the derivative: d dx e² [ In In(1+√7) dt =

A: Since you have asked multiple question, we will solve the first question for you as per our guide…

Q: Use this definition to find f ′(a) at the given number a. f(x) =    6x + 7,    a = 7

A: Solution: Here  f(x)=6x+7 Derivative w.r.t  x ,we get

Q: Find the exponential function f(x) = Ca* whose graph is given below. 2 0 ƒ(x) = (², 3) X

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Q: A particle moves along the path y = 3x² − x³ with the horizontal component of the velocity equal to…

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Q: Suppose that a deer population grows logistically while being harvested at a rate proportional to…

A: Given : Suppose that a deer population grows logistically while being harvested at a rate…

Q: ind the exponential function f(x) = Ca which atisfies the following conditions: (3) (x) = 1 9 and…

A: Given query is to find indicated exponential function.

Q: Step 1 of 4: Find lim f(x). x→4 10 -5 Ay 10 5 Enable Zoom/Pan X

A: NOTE: Refresh your page if you can't see any equations. .

Q: Step 2 of 4: Find lim f(x). x-4+ 10 -5 Av 101 Enable Zoom/Pan 5 10 X

A: NOTE: Refresh your page if you can't see any equations. .

Q: Evaluate the integral. (Reme J dt ²-2t + 17

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Q: Given the points (-2,-4) and (-4, 2), find the rate of change between the points. Answer = (Round to…

A: Given :Points : -2, -4  and  -4, 2

Q: A body was found in the basement of the Underwater Basket Weaving Building at 12:00 noon today,…

A: Given :Newton's Law of cooling -Tt=Ta+T0-Tae-ktT= body temp at tTa=Surrounding's temp

Q: In t years, the population of a certain city grows from 500,000 to a size P given by P(t) = 500,000…

A: By the answering guidelines of Bartleby, We can answer only first three subparts, please post other…

Q: Calculate the limit algebraically. (If an answer does not exist, enter DNE.) x² + 11x + 10 x² + x…

A: let  A=limx→-1x2+11x+10x2+xif we put x=-1, A=00 form there for use l'hopital rule ∂xn ∂x=nxn-1∂…

Q: Suppose A is a 5 x 5 matrix, and that 6 € R5 has the property that A = Explain why the columns of A…

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Q: Show steps to receive full credit. 1. Determine the exact value of the following. (a) sin (105°) (b)…

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Q: Evaluate the integral [[(+²) i + (5) j+(3t+3) k] dt. 0

A: To evaluate the integral of given vector function

Q: J = (x)\, mil 6. Find an equation of the tangent line to the curve y = √ at the point (4,2).

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Q: 1. Determine an equation in factored form for the polynomial function represented by the graph. ✓✓…

A: We have given graph of the function  From given graph  Zeros : -2,0 x=-2 (multiplicity 2) x=0…

Q: 2) Determine 3TT b. 23sin²2x dx

A: INTRODUCTION For any continuous function, f(x) which is defined on the closed interval, say [a,b],…

Q: Question 1 h (x, y) = 2xy + 3x² + 4x³y² + 8 What is the value of Əh(x,y) ду when x = 1.4 and y =…

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Q: Find the distance between the skew lines with parametric equations x = 1 + t, y = 1 + 6t, z = 2t,…

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Q: Let f(x) 3x2+6. Evaluate lim h→0 f(4+h)-f(4) h

A: Solution ⇒     f(x)=3x2+6    and we have to perform  limh→0f(4+h)−f(4)h    Now put…

Q: I. Find the solution of the following differential equation: 1.-4+3y=2; y(0) = 1, y'(0) = 1

A: To find the solution of the following differential equation. d2ydt2-4dydt+3y=2; y0=1, y'0=1

Q: Let M = Mu = ( Mv = ( 3 51 21]. u = (x, y), v = (z, w). Find the following. -3 2

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Q: A population of bacteria follows the continuous exponential growth model P(t)=Poe, where t is in…

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Q: The gravitational pull between a planet and its star causes the planet to orbit its star with an…

A: Givena(t)=4sint,7costv(0)=-4,0r(0)=0,-7   We are required to findv(t)   The following formulas has…

Q: Use the Integral Test to determine if the series shown below converges or diverges. Be sure to check…

A: To show whether the given function converges or diverges.

Q: x³+3x 7. Compute the limit limx→∞ −²+2° O∞ 0-∞ Oo 312

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Q: Given the point A (4,-3,2) and th plane P: 5x - 4y - 3z = -24. LetL be the line through A…

A: This is question of calculus  Here one plane and one line is given  We have to find line point on…

Q: For a school group, a skating rink charges a flat fee of $50 for skates for the students, plus a…

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Q: Find the unit tangent vector T and the curvature K for the following parameterized curve. r(t) =…

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Q: A bucket filled with sand has a total weight of 15 pounds. You begin steadily lifting the bucket to…

A: F=m*ahere a = g = 32.17 fts2Let bucket lift by x feetand it leaks 0.3 pounds of sand for each foot…

Q: use the following information to eval- uate the given limit, when possible. If it is not possible to…

A: INTRODUCTION A limit of a function is the point at which the function's behavior changes…

Q: Use the method of cylindrical shells to find the volume generated by rotating the region bounded by…

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Q: Use the Fundamental Theorem of Calculus to find the "area under the curve" of f(x) between x 17 and…

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