y = C₁ e²^ + C₂ e²^ + Cze=²

Q: 8) f(x) = x³ + 2.56x² - 3.31x +.89

A: y = x3 + 2.56x2 -3.31x + 0.89 The x-intercept is the point where the function's graph touches or…

Q: 48. A rectangle has area 16 m². Express the perimeter of the rectangle as a function of the length…

A:

Q: For the following exercises, use composition to determine which pairs of functions are inverses.…

A: As per our guidelines we can answer only 1 question so kindly repost the remaining questions…

Q: 3. Determine the slope of the secant to the given curve between the specified values of x. a.y=x²…

A: To find the slope of the secant for the given curve.

Q: Find the rate of change of total profit, in dollars, with respect to time where R(x) = 90x - 0.5x²…

A: Given:  Rx=90x-0.5x2 Cx=40x+4 x=48, dxdt=40 To find: The rate of change of total profit, in dollars.…

Q: (a) If x and y are real numbers and x² - y² = 0, then.x = y. (b) If the integer x is a multiple of…

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Q: Find the limit of the rational function (a) as x→∞ and (b) as x→→ ∞. 4 3 2x + 5x - 1 f(x) = 2 2x -…

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Q: When f is the function defined by S 52 – 4, x < 2, {4x-3₁ 4x - 3, x ≥ 2, f(x) determine if = lim…

A: The answer is in step 2.

Q: 5 [²= 2 (a) the trapezoidal rule sinx) dx, n = 6 sin (√x) a

A: Trapezoidal rule :-∫abfxdx≈∆x2fx0+2fx1+2fx2+2fx3+..........+2fxn-2+2fxn-1+fxn Here ∆x=b-an

Q: The graph of (x/a) +(y/b) + (z/c) = 1 is a plane for any nonzero numbers​ a, b, and c. Which planes…

A: Let's find given plane of equations.

Q: Find the equation of the plane containing all points equidistant from the points (3,-7, c) and (1,…

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Q: Find the two values of k for which y(x) = ekr is a solution of the differential equation…

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Q: A stone dropped into a still pond sends out a circular ripple whose ft radius increases at a…

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Q: which of the following functions of f  has a removable discontinuity at a? If the discontinuity is…

A: Please see the below picture for detailed solution.

Q: f(x) = 1/2, X f(x) = f(a) - x - a

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Q: f(x) 2 ta 1 -1 if x # 1 if X=1 al

A:

Q: A company produces a special new type of TV. The company has fixed costs of $471,000, and it costs…

A:

Q: Consider the equation below. 4x² + y2 + 4z² - 4y - 32z + 64 = 0 (a) Reduce the equation to one of…

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Q: 1. Evaluate the following limits. a. lim (x²+2x - 5) x→2 b. lim (3 + x² + x + 1) 2 x→-1 c. lim (t³ -…

A: I am going to solve the given problem by using some simple calculus to get the required result of…

Q: Find an equation of the plane. The plane that passes through the point (-2, 1, 1) and contains the…

A: Topic = 3D Geometry

Q: Let F = 5(x + y) i + 2 sin(y) 7. Find the line integral of Faround the perimeter of the rectangle…

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Q: Find the distance from the point s (−4,1,2) to the line x=9t​, y=4t​, and z=4t.  The distance is d =…

A:

Q: 5. Find an expression for a cubic function f if f(1) = 6 and f(-1) = f(0) = ƒ(2) = 0. Answer |f(x) =…

A:

Q: Let P(x) = (x - 1)(x - 2)² (x-3)³. Find the set of r such that x (a) P(x) = 0, (b) P(x) 0.

A:

Q: (A) Find the slope of the line that passes through the given points. (B) Find the standard form of…

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Q: 41. f(x) = e, a = 3

A:

Q: Find the critical points, domain endpoints, and local extreme values for the function. x={= y =…

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Q: D(x) = 1000 15x is the price, in dollars per unit, that consumers are willing to pay for x units of…

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Q: Find the parametrization for the line segment joining the points ​P (0,8​,9​) and ​Q (0,−8​,9​).…

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Q: Determine whether the lines L₁ : r(t) = (−3,−2, 0)t + (3, —2, 2) and L2: p(s) = (3, 2, 1)s + (−9,…

A:

Q: Suppose that f(1) = 1, f(4) = 9, f '(1) = 6, f '(4) = 4, and f" is continuous. Find the value of…

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Q: Set up a double integral to find the volume of the solid region bounded by the graphs of the…

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Q: Is the line x=5−9​t, y=8+4​t, z=−8t parallel to the plane 3x+y−z=10​? Give reasons for your answer.…

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Q: b) A farmer wants to put a fence around a rectangular paddock which is part of his block (see…

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Q: Problem 7. Find a parametrization of the curve of intersection of x = cos(z) and y = sin(z) from (1,…

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Q: An object moves with velocity as given in the graph below (in ft/sec). How far did the object travel…

A: Concept - Area under the v-t curve from t = a to t = b gives distance covered by the particle in the…

Q: 15. Find the area of the figure below which has three 75.0 mm diameter holes drilled out. 784mm оо…

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Q: пn n!

A: We have to find the limit value .

Q: a. lim (2x + 3) x-5 b. lim (-²+3x − 2) - x-2 c. lim 5(t-2)(t-3) t→-1 x+3 x 3 x 2 d. lim e. lim 2(2x…

A: limit

Q: Checking correction of the indefinite integral, & fxcos x dx-xsin x+cosx+C b. xsin x dx--x…

A:

Q: Evaluate the line integral 5xy² ds, where C is the right half of the circle x² + y² = 9.

A: Evaluate line integral

Q: The functions fand g are defined as follows. f(x) = 2x³ +6 g(x)=-3x+2 Find f(-3) and g (5). Simplify…

A: Topic = Functions

Q: 19. Which of the following expressions will make the statement (0) A = cscx true? sinx, A. A = cotx…

A: Let's solve given trigonometric equations.

Q: Which of the following integrals will determine the area of the region bounded by the graphs (see…

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Q: Let F(x, y) = = 8Q A. Compute dz -yi+zj z² + y² ар B. Compute By and let C be the circle r(t) =…

A: Given function:- Fx,y=-yi+xjx2+y2 and C be the circle rt=costi+sintj

Q: A cone-shaped paper drinking cup is to hold 20 cm³ of water. Find the height and radius of the cup…

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Q: Find the distance (d) between the planes -2x - 4y + 5z = 39 and -2x - 4y + 5z = 14. d =

A: Given;  -2x-4y+5z=39 -2x-4y+5z=14

Q: Study the continuity of the next function x ² y ² x²y² + (x - y)² ) = { f(x, y) if (x, y) = (0,0) if…

A: Given :fx,y=x2y2x2y2+x-y2if x,y≠0,00if x,y=0,0

Q: Find the plane determined by the intersecting lines. L1 x= -1+3t y=2+2t L2 x=1-4s y=1+2s z=1-t…

A:

Q: 1. Find the sum to infinity for the following geometric progression:  3 - 3/2 + 3/4 - 3/8 + ... 2.…

A: