Consider the curve r(t) = (t² + 1)i + tj + (2t² + 3t)k. What is the velocity? What is the accelera tion? Are they constant?

Q: Determine whether the series is convergent or divergent. If it is convergent, find its sum. (If the…

A: Consider the series Sum of a geometric series

Q: 1. a = (2, 5, −4), b = (1, −2, −3) 2. a = (-1,0, 2), b = (3, 4, −5)

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Q: Seperate the variable and solve the equation 2y (dy/dx) + 2x = 0. Use the initial condition x = 0;…

A: The given equation .The aim is to find the solution with the initial value .

Q: Find the area of the region that is bounded by the given curve and lies in the specified sector. r =…

A: r=eθ,3π4≤θ≤3π2

Q: 1) State the order of the given ordinary differential equation. Determine whether the equation is…

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Q: Evaluate the second derivative of the function at the given point. Use a computer algebra system to…

A: The function is given byTo determine: The value of the second derivative of the function at point

Q: Math 152 metric IHU 3. In this problem we'll evaluate the integral cos²(z) sin³ (2) dr. (a) First,…

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Q: Solve the equation for x in terms of the other letters. (Enter your answers as a comma-separated…

A: Given data

Q: ·b f(b) − ƒ(a) = f'(a)(b − a) – ſå ƒ"(x)(x − b)dx - a

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Q: An account earns an APR of 4.7% compounded as often as imaginable ("compounded continuously"). The…

A: The given rate is, r=4.7%=0.047 compounded continuously.For the continuous compound, the annual…

Q: If f(x) x = [²₁ 1 = = then ƒ'(x) = ƒ'(−2) = tadt

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Q: f(x)=x²8x² + 5

A: f(x)=x4−8x2+5

Q: Use a linear approximation (or differentials) to estimate the given number sqrt(99.2)

A: SolutionLet f(x)=√x and use the linearization at a=100

Q: Find the vertex, focus, and directrix of the parabola, and sketch its graph. (x - 6)2 = 2(y + 4) = 0…

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Q: Find the critical numbers of the function. (Enter your answers as a comma-separated list. If an…

A: To find the critical numbers of the following function.

Q: Find the interval containing x = 0 where f(x) = 81x - tan(x) is increasing. Write your answer as an…

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Q: Solve the given initial-value problem. y(x) = 2y" + 3y - 2y = 10x² - 4x 13, y(0) = 0, y'(0) = 0 -

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

Q: Evaluate the integral. +C 2x + 9 x² + 6x +34 17 -da

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Q: Find the volume of the region in the first octant bounded by the coordinate planes, the plane x+y=5,…

A: Equation of plane : and equation of cylinder : Find the volume of the region in the first octant…

Q: Describe the x-values at which the function is differentiable. x² y = x² - 49

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Q: Use Rolle's Theorem and a proof by contradiction to show that the function f(x) = 6x³ + 4x - 11 does…

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Q: Determine the inverse Laplace transform: F(s) = 4/s2 - 5/(s + 1)

A: To determine the inverse Laplace transform.

Q: Evaluate the definite integral by interpreting it in terms of areas. 7 (3x - 18)dx 3

A: To evaluate the following definite integral by interpreting  in terms of areas.

Q: Suppose f(x, y) = x² + y² - 8x and D is the closed triangular region with vertices (8,0), (0,8), and…

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Q: for the function f(x)=x^2+ x find the equation of the tangent line to f(x) at x=1 calculus

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Q: 8. Consider the gradph of the function f(x, y) = x² - 5xy given by z = x² - 5xy (a) ( (1,2). Find an…

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Q: Use the quadratic formula to solve the equation. Give two forms for each solution: an expression…

A: The given quadratic equation is

Q: 9. Locate all relative maxima, relative minima, and saddle points of the fol- lowing function f(x,…

A: The given function is

Q: Indicate whether the graph specifies a function. 10 15 10 O The graph does specify a function. The…

A: to identify that the given graph shows a function or not.

Q: Consider the curve r(t) = tcos(log(t))i + tsin(log(t))j. Is the velocity constant? Is the speed…

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Q: ind the limit if it exists. lim (12x+11) elect the correct choice below and, if necessary, fill in…

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Q: Find the equation of the tangent plane to the surface determined by x³y² + z-30 = 0 at x = 3, y = 5.…

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Q: Find a Cartesian equation for the curve. r = 9 cos(0)

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Q: 2. Isolatex. For answer, show this structure <x< -5 ≤ 2-x < 5

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Q: Use partial fraction decomposition to find the following integral -da 24-1

A: I=∫x2x4−1dx

Q: Determine if the series diverges. If it does diverge, type a upper case D as your answer, and if the…

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Q: Sketch the graph of f by hand and use your sketch to find the absolute and local maximum and minimum…

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Q: 2. Determine whether the series n Σ» (-1) (3) converges or diverges. If it converges, find the sum.

A: The given series is

Q: The median home value in Texas and Missouri (adjusted for inflation) are shown below. Year Texas…

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Q: Differentiate the function. X f(x) = - 1 Xx +9

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Q: question e,f

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Q: Isolate 9.\ 2 5 = 22 gt² + vt gt² + avt ??? 25 = 25= 2 ut(+ +2 g = expected: -avt + $25 t²

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Q: Express each function as a composition of two functions. (Find f(x) and g(x) such that the given…

A: We have to find the given function as a composition of two functions f and g.

Q: Find the domain of the function. h(u, v) = √3-u² - v² Ou+v≤3 Ou² + v² 0 Ou+v<3

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Q: Find the maximum and minimum values of f(x, y) = xy on the ellipse 5x² + y² = 4. √20 maximum value…

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Q: Find the slope of the tangent line to the given polar curve at the point specified by the value of…

A: The equation of the curve is given byTo determine: The slope of the tangent line to the given curve…

Q: Find the limit if it exists. lim (5x+8) x→-5 Select the correct choice below and, if necessary, fill…

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Q: 17. x1 - 3x2 + 2x3 - 4x4 = = 0 2x1 - 5x2 + 7x3 − 3x4 = 0

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Q: Solve the following non-homogeneous differential equations: x" (t) + x(t) = 2 cost 1) -X 2) y"+2y+y…

A: The given differential equation is; x2y''-2xy'+2y=xlnx

Q: Evaluate the following limit. lim x→0 3 (²2 x 3 sin(2))

A: L=limx→0(3x−3sin⁡(x))