Find a parametric description r(t) for the following curve. The line segment from (6,4,8) to (5,8,13) r(t) = for 0 st≤ 1

Q: 2. Use the first derivative test to locate the local maximum and local minimum point(s). f(x) = -x³…

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Q: Find the gradient field of the function, g(x,y,z) = e² - In (x² + 4y²). ¹= Di + i + Dk. The gradient…

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Q: Let r(t) = (-4t + 4, e¹, 5e¹¹). Find the line (L) tangent to r(t) at t = L: (x, y, z) = Question…

A: We need to find Tangent Line

Q: Given the vector-valued functions i(t) = et + et + 5tk (t) = 3ti + 3t²j5k d ind(u(t) (t)) when t =…

A: Given vectors:- u→t=e5ti+e-4tj+5tk v→t=3ti+3t2j-5k

Q: 1) 225° Quadrant Reference Angle Cos 225º =

A: given angle is  2250 since we know that if angle  θ∈[1800 , 2700 ]then   angle θ lies in quadrant…

Q: Find and classify any critical points. 3. z = 4xy - x4-y4

A: for critical points put ∂z∂x=0 and ∂z∂y=0∂xn∂x=nxn-1

Q: A particle moves in a straight line with the given velocity v(t) = 36t−² − 1 (in m/s). Find the…

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Q: For Problems 3-4, find the definite or indefinite integral, giving an exact answer for a definite…

A: Since you have asked multiple questions in a single request so we will be answering only first…

Q: 3.)  This is differential Calculus subject. A PARTICLE IS MOVING ALONG A HORIZONTAL LINE ACCORDING…

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Q: 9. a javelin thrown at 65 feet per second at an angle of 60° with the horizontal

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Q: could you please simplify what it means after the third U in both answers . like write it in another…

A: Please see the answer.

Q: A ball is thrown upward from a height of 2 m at an initial speed of 40 m/s. Acceleration resulting…

A: Let's find velocity and height function.

Q: Find the exact length of the curve. y = √x - x² + sin-¹ (√x)

A: The given curve is: y=x-x2+sin-1x

Q: Unless specified, all approximating rectangles are assumed to have the same width. Evaluate the…

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Q: b. lim 2 sin(x-3) x²-3x

A: The given limit limx→32sinx-3x2-3x. We have to find the limit.

Q: Σ(3)" n=1

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Q: Give a possible formula for the function below. Let A = (1, 6) and B = (2, 18). Use the general…

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Q: x Let g(x) = ™* sin(t)e'dt. Then g'(x) equals 2 sin(x)e None of these options are correct. sin(t)et…

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Q: Use the limit definition of the definite integral to determine the value of the definite integral…

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Q: (s² – 1)³ 56 F(s)-¹ 1-1 {(8²50 e + -TTS – - 2πS s² (s — 4)

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Q: Use the table to solve. X g(x) -2 1 5 a. (f+g) (4) = = B. (f-g) (2)- c. (²₁₂) (-2) = d. f - O to O 2…

A: To find the value of given functions

Q: 214 (a) Estimate the area under the graph of the function ƒ (z) — _—_—__ from 2 – 0 to z – 1 using a…

A: Solve the following

Q: Convert y = 29 z² to polar coordinates in the form: r is a function of 0. r =

A: Given,            The rectangular coordinates is y=29x2.To find : Convert rectabgular to polar…

Q: Find the domain of y = log(4 - 3x). The domain is: Ox≤ A Ox> A Ox ≥ A 0x<A where A = 3x X syntax…

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Q: -2 0 8 4 Determine the x-value where a possible global maximum for a function h occurs on the…

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Q: Given that f(x) = x³h(x) - h(1) = 5 h' (1) 8 = Calculate f'(-1).

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Q: Find the area of the shaded region y = x(x-4)² y = x

A: The region is bounded by the curves y=xx-42 and y=x. We have to find the area of the shaded region.

Q: Use a suitable change of variables (i.e., substitution) to evaluate the following integral. Hint:…

A: First I have made some change in the integrand by using trigonometric identity and then by suitable…

Q: A wire of length 7 is cut into two pieces which are then bent into the shape of a circle of radius r…

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Q: 3. Tim ( x ²-1 x2-3x+2/

A: use L'hospital rule limx→1(x2-1x2-3x+2)=limx→1∂ ∂x(x2-1)∂ ∂x(x2-3x+2)∂xn∂x=nxn-1

Q: Evaluate the integral SSSR x² + y² + z² dV where R is the region bounded above by the paraboloid z =…

A: Let's evaluate the given integral.

Q: Suppose that the monthly marginal cost for firefighting portable water tanks is C'(x) fixed cost of…

A: To solve the following problem

Q: Find an equation of the ellipse with the following characteristics, assuming the center is at the…

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Q: At a computer store, a customer is considering 6 different computers, 8 different monitors, 9…

A: The answer is given in step 2   Topic: Multiplication rule of counting

Q: 1. Over a 3-hour period between noon and 3 pm, the rate of temperature increase in a town is given…

A: We need to estimate integral.

Q: Use a series to estimate the following integral's value with an error of magnitude less than 10 -5…

A: We need to estimate integral.

Q: 4. What is the slope of the tangent to f(x)=√√x-1 at (5, 2)? c. 2 14 12 a. 1 b. 1 d. 4

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Q: Find the net signed area between the curve of the function f(x) = x³ and the x-axis over the…

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Q: b) Suppose that w = x2 + y² - z2 and_x = p sin + cos0, y = p sin ф sin 0 , z = p cos ф Əw aw find…

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Q: Find an equation for the tangent line to f(x) = 2x³ - 6x² + 8x - 1 at x = 2. y = 7(x - 2) Oy=7x…

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Q: 1. Evaluate the line integral where C is the half circle x² + y² = 1, y ≥ 0. 1²+y² ds

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Q: Use the graph shown to find the following (a) The domain and range of the function (b) The…

A: We need to interpret the graph.

Q: Find the area of the region enclosed by r = Provide your answer below: A = 26 sin(0). Enter an exact…

A: NOTE: Refresh your page if you can't see any equations. . take r=0 so lower and upper limits…

Q: Suppose that the monthly marginal cost for smokejumper harness straps is C'(x) = 3.5x +95 and the…

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Q: 3. [11.9] Find a power series representation with center at x = 0 for the functions and determine…

A: Solve the following

Q: 1. Plot 1/(x^2-1), x/(x^2-1), x^2/(x^2-1), x^3/(x^2-1) when x = -2 to x=2.  2. What are the…

A: We have to plot graph of Gven Functions,1x2-1, xx2-1, x2x2-1, and x3x2-1.,From x = -2 to x=2.

Q: Show that the differential form in the integral is exact. Then evaluate the integral. (0,1,2) S…

A: Note:- Since you have asked multiple question As per our policy, we will solve the first question…

Q: 2. Use the first derivative test to locate the local marimum and local minimum point ( f(x) =…

A: we need to use the first derivative test to find out the local maximum and local minimum points.

Q: 5.) USE IMPLICIT DIFFERENTIATION TO FIND dy/dx. WITH THE GIVEN EQ’N: x^3 y^3 + x cos y = 7.

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Q: Translate the given system of equations into matrix form. x + y = z = 6 7x + y + z = 4 3x + N|M =…

A: To translate the given system of equations into matrix form.x+y-z=67x+y+z=43x4+z3=1