Find the unit tangent vector to the curve defined by 7 r(t) = (5 cos(t), 5 sin(t), 2 sin² (t)) at t = 6 T(-²) = .

Q: Evaluate f(x, y, z) dV for the specified function f and B: JB f(x, y, z) dV = f(x, y, z) = Z x 2 ≤ x…

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Q: Evaluate the following indefinite integral. Show all intermediate steps. fx√x+1 dx

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Q: The function f is shown below. What is the value of answer in simplest form. -10-9-8 5 4 3 2 11 8 6…

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Q: Find the indicated value. f(5,2) if f(x,y)=2x²y-5xy³ f (5,2)= 10 (Type an integer or a simplified…

A: Given a function fx,y=2x2y-5xy3 We have find the value of fx5,2 Derivative of a polynomial function…

Q: 1 Find the Taylor Series generated by f(x) = (7-X)⁹ at X=6 9 (7-x) 10 f'(x) = 90 f"(x) = (7-x)" f(x)…

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Q: An arithmetic sequence has first term a = 5 and common difference d = 4. How many terms of this…

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Q: 1 f(x) =(√² + √2)²

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Q: For a cost function, f(x, y), the minimum cost for a production of 56 is given by f(49, 84) = 1400,…

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Q: 1.3: The derivative of the function sin(cos x) is a) cos(cos x) b) cos(-sin x) c) sin x cos(cos x)…

A: The given function is: fx=sincosx As we know from the Chain rule: fgx'=f'gx·g'x And the common…

Q: Consider points A(4, -1, 3), B(3, 1, 6), and C(1, -3, -3). (a) Find the area of parallelogram ABCD…

A: The given problem is solved below in detail.

Q: Q6. Evaluate S¹, S₂ Sp dz dx dy.

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Q: Find the area of a triangle PQR, where P = (-4, -2,-2), Q = (-5, 2, 5), and R = (-2,5,-4) Check…

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Q: A spherical iron ball 8cm in diameter is coated with a layer of ice of uniform  thickness. If the…

A: Given data:- The diameter of the iron ball is, 8 cm The thickness of the coating is, 2 cm The rate…

Q: Q2. Find the second order partial derivative of x² - y² + 2xz - xy + yz.

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Q: The figure below shows contours of f(x, y) and the constraint g(x, y) = c. Approximately what values…

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Q: Evaluate: (In x)² x -dx - +C

A: Topic - indefinite integral ∫xndx=xn+1n+1+C

Q: 76 6 27 6 Σ [5 (2 + (i - 1) =) * - 7 (2 + (x − 1))"] n n as a definite integral, that is provide a,…

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Q: Find the partial sum S, of the geometric sequence that satisfies the given conditions. 2 3 S4=…

A: Please see the below picture for detailed solution.

Q: where does xk come from

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Q: 1 2 ¹/² (²1-5) dz. Write a limit using summations that would equal

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Q: tim X-1 2 x² + ax +b = 2 find 9, and b a, X² + X=2

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Q: Use the rules for sums of powers of integers to compute the sum. 24 4.² k=8

A: Recall: sum of squares of n integer                    ∑i=1ni2=n(n+1)(2n+1)6

Q: Find the particular antiderivative of the following derivative that satisfies the given condition.…

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Q: The function f is shown below. What is the value of nswer in simplest form. -8 -3 N 3 H N W 4 in -5…

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Q: Find the future value at 5.25% interest, compounded continuously for 5 years, of the continuous…

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Q: Find the first four partial sums and the nth partial sum of the sequence an 2 30 an =

A: Given function is an=23n Here, we have nth term of series Evaluate the first termS1, substituting…

Q: dx 3 sin x-6 cos x

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Q: (b) Sketch, on separate graphs, each of the following functions (ii) sech(x). (iii) coth(x).

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Q: Evaluate the definite integral using Part 1 of the Fundamental Theorem of Calculus. 6² Enter the…

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Q: Centerville is the headquarters of Greedy Cablevision Inc. The cable company is about to expand…

A: Centerville is located at 10,0 in the xy-plane Springfield is at 0,5 Shelbyville is at 0,-5 The…

Q: How long will it take for an investment of $3000 to double in value if the interest rate is 6.5% per…

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Q: Differentiate the following function. You do not need to simplify the derivative. h(x) = 2x²ellz…

A: Topic = Derivative

Q: 5. The movement of the crest of a wave is modelled with the function h(t) = 0.2 cos(4t) + 0.3…

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Q: For the function f(x,y) = 7x² + 6y², find f(x + h,y)-f(x,y) = h f(x+h,y)-f(x,y) h

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Q: Find the integral of f(x) = 1 √1-16x² between 0 and 1.

A: The given integral is 1/sqrt(1-16x2).

Q: Solve the differential equation dy dx 9xy - 2y² 6x² xy O a. 3y³ O b. 3x³ x²y = 2y² x²y = 2y² O c.…

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Q: 1. Let f(x, y) = y²exy. (a) Find the normal vector to the graph of f(x, y) at (0, 1, 1).

A: Please see the below picture for detailed solution.

Q: 8. [In(x² + 1) dx

A: Formula for Integration by parts: ∫fg'=fg-∫f'g

Q: Convert from polar to rectangular coordinates (0, 7/7) (Round your answer to 2 decimal places where…

A: Part iGiven,            0,π2

Q: 1.5: The area of the region enclosed by the graph of f(x)=√x and the x- axis on the interval [0, 4]…

A: To find area

Q: face da +C

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Q: Find the nth term of a sequence whose first several terms are given. 10 11 9' 10' 11' 12' an = Need…

A: The given sequence is 89,910,1011,1112,....

Q: Prove, using the definitions of tanh and sech in terms of the exponential function, that 1 − tanh2…

A: Substitute the exponential function of tanhx in the equation

Q: Find the following limit. lim

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Q: Let P be the set of positive real numbers. One can show that the set P³ = {(x, y, z)|x, y, z € P}…

A: The objective of the question is determine the vector .

Q: Find the intervals on which the graph of f is concave​ upward, the intervals on which the graph of f…

A: f(x)=-x4+16x3-16x+5 If a function is concave up then f"(x)>0 If a function is concave down then…

Q: x Cothx Y = (Sink x) 4 Find dry" dx [ Sin'x]

A: Given: y=sin hxx cot hx

Q: Use basic identities to simplify sin³ x + x + cos²x sinx. Enclose arguments of functions in…

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Q: sec 2(t)- 9t2 Justify your response. b. Find the antiderivative of f(t) = s

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Q: Find the linearization of the function f (x) = x³ at x = 1. L(x) = Using this linearlization, ƒ…

A: Answer is in next step.