Sketch the space curve. Vector-Valued Function r(t) = -ti + 2tj + 6tk ** kk Find its length over the given interval. 2 Interval [0, 1] 2

Q: Use Newton's method to approximate a root of the equation 4x³ + 2x + 4 = 0 as follows. Let x₁ = 1 be…

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Q: Use Definition 7.1.1, DEFINITION 7.1.1 Laplace Transform Let f be a function defined for t≥ 0. Then…

A: Given figure:-

Q: Use the Laplace transform to solve the given initial-value problem. y""+ 2y" -y - 2y = sin(4t), y(0)…

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Q: Find the exact value of the trigonometric expression given that sin(u) = -3, where 3π/2 < u < 2π,…

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Q: Find the absolute maximum and minimum values of the function over the indicated interval, and…

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Q: 5. If y = t^2+2 and x = 3t + 4, find dy/dx.

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Q: A company manufactures and sells x cellphones per week. The weekly price-demand and cost equations…

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Q: Evaluate foxy dx dy. Round your answer to two decimal places. O 12.64 29.50 O 105.35 O 26.34 O88.49

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Q: Solve the following equations. 1) tan² x + 2 secr-7=0 if re [0, 2π)

A: We have to solve the equation tan2x + 2 sec x - 7 = 0   if  x ∈ [ 0, 2π).

Q: Find the absolute maximum and minimum, if either exists, for the function on the indicated interval.…

A: Topic- absolute maximum and minimum of a function

Q: Parametric Equations X = 3t², y = 3√t 54m 12 Jse a graphing utility to approximate the integral.…

A: The solution is given below

Q: Which one of the following is an antiderivative of the function f(x)=sec² (2x+1)

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Q: Consider the problem √√²-1 da If we try to solve using integration by parts, we might choose น= x² -…

A: Given integral:- ∫x2-1xdx

Q: Convert the point (3, −3) in rectangular to polar coordinates (r, 0). 7T 18, (7) 3√2,

A: NOTE: Refresh your page if you can't see any equations. . the given point is

Q: Find dy/dx: 1 II 22²+(²+1)¹

A: Important Formulae:1)ddx(xn)=n xn-12)ddx(1x)=-1x2

Q: a f'm f(x) dx for the function f(x) graphed below. [Hint: No calculus is necessary-just as we used…

A: We can find the value of integral  of a function f(x) by using the area under the curve f(x).

Q: For the function f(x,y)=−5x2+2xy+3y2−x−5y+1f(x,y)=-5x2+2xy+3y2-x-5y+1, find a unit tangent vector to…

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Q: a)lim              (e^-x)(x^2+sinh(x+2))    x->∞   b) Find the point where the tangent to the…

A: find limit solve the parametric equation

Q: Calculate the present value PV (in dollars) of an investment that will be worth $1,000 at the stated…

A: Given the query is to find the present value of the investment.

Q: Evaluate the line integral curve C : x = 4 cost, y = 8 sint (0 ≤ t ≤7 < NOTE: Enter the exact…

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Q: The position vector r describes the path of an object moving in space. Find the velocity v(t), speed…

A: Given: r(t)=etcost,etsint,et

Q: A solid is generated by revolving the region bounded by the following about the y-axis. y = y = 8 A…

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Q: At the beginning of every three months, a college student deposits P3,000 in a fund that gives 2%…

A: Given:      Principal =$3000     Quarterly Interest rate =2%=2%4=0.5%=0.005     number of times n=3…

Q: Find the nth Taylor polynomial for the function, centered at c. P4(x) = f(x) = 1 +2, n = 4, c = 5

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Q: Find the specified nth term in the expansion of the binomial. (x - y)², n = 2

A: We need to find nth term.

Q: Write an expression for the apparent nth term an of the sequence. (Assume that n begins with 1.) 4 5…

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Q: Determine the height h above the base of the centroid of the cross-sectional area of the beam.…

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Q: dy Find at x = dt dy dt || 4 if y = 3x² + 5 and dx dt = 1.

A: Let's find dy/dt value at x=4.

Q: Use Theorem 7.1.1 to find {f(t)}. (Write your answer as a function of s.) f(t) = (3t-1)³ L{f(t)}

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Q: repres

A: Equation of least squares line is given as                            Y = A*X + B, Where,…

Q: For the function f(x,y)=(4−x^2−y^2)/−5, find a unit tangent vector to the level curve at the point…

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Q: Use the Fundamental Theorem of Calculus to find the "area under curve" of f(x) = 8x + 4 between x =…

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Q: The second derivative has been found and already factored to be f(x) = (3-x)(x+6). interval testing…

A: NOTE: Refresh your page if you can't see any equations. . the second derivative is given by

Q: Use appropriate algebra and Theorem 7.2.1 to find the given inverse Laplace transform.(Write your…

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Q: d the following for the given equation. r(t) = (et, 6t², 8 tan(t)) (a) r(t) = (b) r"(t) = (c) Find…

A: Topic:- application of derivatives

Q: Use implicit differentiation to find an equation of the tangent line to the curve at the given…

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Q: Find a unit normal vector for the following function at the point P(−4,3,−64)P(-4,3,-64):…

A: We have to find the unit normal vector of the given function.

Q: Summarize all pertinent information obtained by applying the graphing strategy and sketch the graph…

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Q: Exercise 2. Plot the graph of the function given in polar coordinates tanh 0-1 r = 2 Write analysis…

A: Given: r=2tanθθ-1since θ&gt;1(radians)

Q: (1) Consider the following integral 1-y² LI /2-x²-y2 1 x²+y² x² + y² + 2² (a) Convert the integral…

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Q: Find the absolute maximum and minimum values of the function over the indicated interval, and…

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Q: Consider the graph of the function g given by g(x) = n(x2+1) for 0 0. 0.81 0.6 0.4 0.2 0 20 40 60…

A: Given data:- The given function, g(x)=ln(x2+1)x         for (0&lt;x)

Q: Q5: a\State and prove the theorem of (continuity-differentiability), then find the value(s) of x…

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Q: Complete the squares and locate all absolute maxima and minima, if any, by inspection. Then check…

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Q: The region bounded by f(x) = - 2x² + 8x + 24, x = = 0, and y = the volume of the solid of…

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Q: Use the given conditions to find the exact values of sin(2u), cos(2u), and tan(2u) using the…

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Q: Write the first five terms of the geometric sequence. a₁ = 2, r = n a1 a2 N 33 24 a5 = = = =

A: Solution of given question is written in below steps.

Q: Find the area of the region common to the circles r=-6 sin 9 and r= 3.

A: answer is in next step. please give a like !!

Q: A 4-pound weight stretches a spring 2 feet. The weight is released from rest 20 Inches above the…

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Q: Find the standard form of the equation of the ellipse with the given characteristics and center at…

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