Express x = t + 6, y = 2t + 2 in the form y = f(x) by eliminating the parameter. y =

Q: Determine the graph corresponding to the given vector equation. r(t) = (6t)i + (42-6t)j, 0≤t≤7…

A: Let's solve vector value function and integral.

Q: 105 105 Suppose that a₁ = -7 and b₁ = -30. Compute the sum. i=1 i=1 105 Σ (19a; - 17b;) i=1

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Q: Find the arc length of the curve on the interval [0, 2л]. Hypocycloid perimeter: x = a (cos(0))³, y…

A: formula for arc length is  L=∫02π(dxdθ)2+(dydθ)2dθ∫sinθdθ=-cosθ+cdxndx=nxn-1

Q: 1. Let x = t-1, y = t² - 2t a. Eliminate the parameter and write an equation in rectangular…

A: To eliminate the parameter and form equation in rectangular coordinates

Q: 2. Find an equation for the tangent line to the graph at the specified value of x.. y=x'sin 4x at x₁…

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Q: Given f(x) = 7x² − 12x + 11. a. Find f'(x). f'(x) = b. Find the slope of the line tangent to the…

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Q: (D² + 1)y = − 2x + cos2x.

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Q: formula Use the appropriate compound interest to find the amount that will be in each account, given…

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Q: Let f be the function given by f(x) = −4|x|. Which of the following statements about f are true? 1.…

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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: Find the minimum and maximum values of the function f(x, y) = x² + y² subject to the given…

A: The function fx, y=x2+y2 subject to the constraint x4+y4=2. We have to find the maximum and minimum…

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

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Q: -2 0 1 O: 2 Find the absolute maximum of f(x)=√√4x2² on [-2, 2].

A: Here we have to choose the correct option.

Q: The function f(x) = x² +9, x ≥0 is one-to-one. (a) Find the inverse of f and check the answer. (b)…

A: Given: f(x)=x2+9

Q: The marginal profit, in dollars from drilling a well that is x feet deep is given by P'(x) = 3. Find…

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Q: The rate of emission, E, in tonnes per year, of pollution from all factories in a certain country is…

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Q: 4. Find the limits. a. lim (x²−1) ln(1-x² )

A: Find the limit using L hospital rule

Q: Evaluate the following integral using a change of variables. y-x !!()** y + 2x + 1 R تالي y-x y + 2x…

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Q: Find the minimum and maximum values of the function subject to the given constraint f(x, y) = 16x² +…

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Q: 15. Which of the following is a point at which the tangent to y = (x − 2)²(x + 3) is horizontal?…

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Q: 5) y=sin (0-60) 90° 180° 270° 360° 450° 540°

A: Note:As per our guidelines we are supposed to answer only one question if there are multiple…

Q: Consider the function f(x) = 5x² - 6x +9, 0≤x≤9. The absolute maximum of f(x) (on the given…

A: ginen  f(x)=5x2-6x+9for critical points put f'(x)=0dxndx=nxn-1

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: 12. Let f be the function given by f(x) = 3e2x and let g be the function given by g(x) = 6x³. At…

A: here given function f(x)=3e2x and g(x)=6x3 if the graph of function f and g have parallel tangent…

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: x/6 S 0 cos 9x dx

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Q: ΔΔΔΔΔ . α) use substitution and the evaluation theorem to calculate the followin integral δε 1 xl…

A: Since you have posted multiple questions i can do first question as per our company guidelines…

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: Find the gradient vector field of f. f(x, y) = xe5xy Vf(x, y):

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Q: 6. The slope of the line normal to the graph of y = 2 In(secx) at x = is

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Q: sin(4x) (b) lim 2-0 tan(x)

A: Given limx→0sin4xtanx apply  L'Hospital rule limx→0cos4x4sec2xapply limit cos(4×0)4sec2(0)=141…

Q: Determine whether the series converges, and if so find its sum. Enter the exact answer as improper…

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Q: A graphing calculator is recommended. Use a graphing calculator to graph the solution of the system…

A: Solution: Given data, y ≥ x3    2x + y ≥ 0 y ≤ 2x + 5

Q: ferinz 6.³ cos xdx esin x www cos xdx hace values. +C

A: Let's solve given integration.

Q: An oil storage tank ruptures at time t = 0 and oil leaks from the tank at a rate of r(t) =…

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Q: Let A be a 2 x 2 square matrix such that 2 ^ (₁)-(₂), and 4 (²)-(3) A A 2 det(A). Hint: find the…

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

Q: Find the average value fave of the function f on the given interval. f(0) = 7 sec²(0/6), [0, 37] 2…

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

A: As we know that, The Power rule: ddxxn=nxn-1 The Product rule: f·g'=f'·g+f·g'   The given equation…

Q: Evaluate 2 O evIn(5) 1 S ○ 1 5 0 In(5) 1 2 dư. (evin (5) – 1)

A: Let's solve given integral.

Q: Suppose g is differentiable for all x, with g(1) = 0 and g(4) integral is equal to sin ¹(4) ㅠ 2 0-2…

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Q: Use an appropriate test to determine whether the series converges. 8 k! Σ k=1 5 k Select the correct…

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Q: Find the length of the curve over the given interval. Polar Equation Interval r = 2a cos 0 9π X π π

A: To find length of polar curve.

Q: 9. (1+ sin 0) de

A: To evaluate the given integral

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 indefinite integral. X LA 1-X dx

A: Let's solve indefinite integral.

Q: Question 25 Determine the correct end behavior of f(x) = -4x³ - 2x²+2x+3 A B C falls to the left and…

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Q: If the marginal cost for ski gloves is C'(x) = 5.5x + 10.5 and C(0) = 351, find the cost function…

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Q: c4 (ex + √x) dx

A: Given query is to find the value of the integral.

Q: i need the asymtotes of the function on the domain

A: The given function is  px=tanx-π3.