Determine the interval(s) on which the vector-valued function is continuous. (Enter your answer using interval notation.) 1 r(t): i + 31 6t+1 =

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A: If the roots of the auxiliary equation are complex α±iβ , then the complementary function is…

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A: Let's find.

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A: Given that region is bounded by the curve y=x and y=x2first find the intersetion point of the curves…

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Q: Let f(x) = 31² - 20x + 25 2x² + 12 - 1 This function has: 1) A y-intercept at the point 2)…

A: Given that    f(x) = (3x2-20x+25)/(2x2+1x-1)

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A: We need to find derivative.

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Q: Question 9 A phone company charges for service according to the formula: C(n) = 22 +0.07n, where n…

A: A phone company charges for service according to given function .     [ C(n)= 22 + 0.07n ] Where,…

Q: 1. Evaluate the following limits. L'Hopital's rule is NOT allowed. 2-√√x-1 1. lim x-5 x² - 4x - 5 2x…

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Q: b) Find the mixed partial derivative at the point (1, 2). g(x, y) = sin(x) In (2y) + y ln(x) + 2xe³x…

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Q: dx Arcsin (²) + c

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Q: I. Evaluate the following limits. Using L'Hôpital's Rule is not allowed. 3. lim (x-3) tan(9-x²)…

A: Formulas of limits which have been used are written in the solution

Q: Calculate the derivative. x4-4 y = x²5 (Give an exact answer. Use symbolic notation and fractions…

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Q: Find the domain of r(t) and the value of r(to). NOTE: Round your answer to two decimal places when…

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Q: Identify the surface that corresponds to the equation 100y^2 - 25x^2- 4z^2 = 1. O elliptic…

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Q: 7. f(x) = 3√x; [1,4] 8. f(x) = x-2/3; [1,27]

A: We can solve this as follows:

Q: Do as indicated. 1 1. Let f(x) = Find the equation of the tangent line to the graph of f'(x) at the…

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Q: Find all real solutions of the equation 8m² -18-374. Write your answers as a list, using a comma to…

A: A detailed solution is given below

Q: 15x²x³43x - 19 The integral (x + 1)²(x² - 6x + 13) Ax + B What is the value of dx ? ax²+bx+c 31 -…

A: Given integral ∫15x2-x3-43x-19(x+1)2(x2-6x+13)

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A: Explained below

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Q: π/4 x³ dx (x²+4)5/2 (Use trigonometric substitution)

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Q: Question 12 Determine the equation of the vertical asymptote and the equation of the slant…

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Q: 1. Three-digit numbers (a) How many repeating three-digit numbers can be formed using the numbers…

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Q: Please solve the problem with complete solution. Thank you

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Q: 1. Evaluate the following limits. L'Hopital's rule is NOT allowed. 4. lim x-∞ 8118 5. lim 1-x+ 2x +…

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Q: Let (A) = and B = . Find the angle between BO and A D O 【cos) 2/√(30(21)) O [cos] ^(-1) 2/√(30(21))…

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Q: The demand for a product is given by D(x) = 150e-0.025x, where x is the number of units sold each…

A: Let's find.

Q: Find the characteristic equation and the eigenvalues (and a basis for each of the corresponding…

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

Q: dx If S = is solved by trigonometric substitution, which of the following x² - 2x - 4 substitutions…

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Q: Find E (p) for the price demand equation and interpret the results. x = f(p) = 1200(50p) where p-$28…

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Q: Find an equation of the tangent line to the graph of y = 2x² + 3 that is parallel to the line 8x - y…

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Q: Consider S 1x². 2-9 x3 what is the integral form in terms of ? A / Scos² e de Ⓡ = sin²e de B C…

A: This question is related to Indefinite integration, we will solve it using given information.

Q: 6x5-25x+8x3+43x²-8x-12 4. Find (3x+-11x² +9x²-11x+6) (9x²+12x+16) -dx if this can be reduced to 63…

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Q: 59-62 Use Part 2 of the Fundamental Theorem of Calculus to find the derivatives. d evi dt sin sin…

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Q: 1 sinx+cosx+1 -dx

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Q: π/4 x³ dx (x²+4)5/2 ST/4 (Use trigonometric substitution)

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Q: List the absolute maximum and absolute minimum of f(x) = x³ 12x on the interval -3, 1]. Give the…

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Q: Consider the partial differential equation u, + uux = 7+ uxx: Determine the order of this equation;…

A: Given differential equation:- ut +uux =7+uxx

Q: Find T(t) and N(t) at the given point. X = = et cost, y = et sint, z=et; t = 0 T(0) = N(0) || =

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Q: Determine the values of r for which the differential equation y' +9y = 0 has solutions of the form y…

A: Given differential equation.

Q: 1. f (5x¹8x³ 2. f (4x + 2) de +6x² - 4x + 7) dx

A: Topic:- integration

Q: If f cos42t dt = At - B sin 2t cos 2t + D sin 4t cos 4t + C where A, B, C and D are constants, ....…

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Q: Find the volume of the solid obtained by rotating about the y-axis the region bounded by y = 2x² -…

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

Q: Choose ALL of the following intervals on which the following function is continuous. 2-4 f(x) = 2²²6…

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Q: d Calculate[ri(t) · r2(t)] and 77[r1(t) × r2(t)] first by differentiating @[r₁(t) the product…

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