37. (grad ƒ) × grad f, (grad f) grad f

Q: * Evaluate. [[6x [6x² arcsin (x)]dx

A: We use integral by parts to solve the given problem.

Q: Find the length of the spiral. r= 502, 0≤0≤ √5 95 19

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Q: Find the unit tangent vector of the given curve. r(t) = (7t cos t-7 sin t)j + (7t sin t + 7 cos t) k…

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Q: Round your answer to the nearest cent.) JHhUity account. HINT [See Quick Example 1 and Example 1.]…

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Q: 1. Find the solution for 2 - 2t+4y=0 with the initial conditions y(0) = 1, y'(0) = 0. (Hint: Try a…

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Q: Find the nth Taylor polynomial centered at c. f(x) = ln(x), n = 4, c = 6 P4(X) =

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Q: Find the general solution of the given system. dx 4x + 5y dt dy = 10x+9y dt (x(t), y(t)) = =

A: The solution of system of differential equation is solved below

Q: 1. (a) Use differentiation to find a power series representation for 1 f(x) = (1+x)² ˚ What is the…

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Q: A and B are matrices, and A~ B. Indicate whether each statement is always true or possibly false.…

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Q: In Exercises 1-4, apply the Jacobi method to the given system of linear equations, using the initial…

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Q: Question 6 Consider the following system ax - bay, -cy + day, where a, b, c and d are strictly…

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Q: (c) Consider the system x'(t) =ay² - x, y' (t) = -y-ax². x' (t)-y-2x, y'(t)=2x-y-x³.

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Q: B 4 3 5 6 1 -2 1 1 4 3 f(x) 1 92. The function f is twice differentiable. Selected values of ƒ are…

A: We can solve this using Newton divided differences method

Q: Find the unit tangent vector of the given curve. r(t) = (7t cost-7 sin t)j + (7t sin t + 7 cost) k…

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Q: Find the general solution to the following equations. 1. x²y" — (y')² – 2xy' = 0

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Q: Find the volume of the solid that results when the region enclosed by the given curves is revolved…

A: Given the region enclosed by the curves x=cosecy, y=17π4, y=19π4, x=0 is revolved about the y-axis.

Q: -1 5 -2 Consider the matrix A= 2 a) Obtain the eigenvectors (v₁, V2, V3) of A. b) Write a matrix P…

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Q: II. Find dy dx 2. y = Do not simplify your answers. tan ¹(cosh x) (sin²x) (sech x)sec a [use…

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Q: y + (cos x) y =3 sinx.cosx

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Q: A car initially sold for $23,999. Its class life is 12 years, and the car depreciates by $750 each…

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Q: Express the limit as a definite integral on the given interval. cos Xi lim Ax, [3π, 5π] 816 X₁ 5m 3m…

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Q: an+1 Assume that converges to p = 1. What can you say about the convergence of the given series? an…

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Q: Find the number of ways to distribute 12 people into 3 classrooms, empty classrooms are allowed.

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Q: Problem 2. (a) Use the long division algorithm to divide x³ +5x+3 by 3x+2 in Z/7Z.

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Q: If FFX f(x) dx = 12 and 1.³ 24 X Enhanced Feedback Please try again. Remember, fr f(x) dx. °F(x) dx…

A: Given ∫15f(x)dx = 12∫45f(x)dx = 5.4

Q: Suppose p is a prime greater than 5. Zop (a) Find the number of generators of the cyclic group (b)…

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Q: Use the method of undetermined coefficients to find a general solution to the system x'(t) = Ax(t) +…

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Q: Eulers Formula states that e^ix = cos(x) + isin(x). when prooving this formula with the given…

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Q: The eigenvalues are A₁ < A₂ <3 < A4, where X₁ has an eigenvector eigenvector = A = -37 15 0 0 -70 28…

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Q: | 1 (25 – x²)³/² dx

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Q: (D² - 1)y= 2 1+ex

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Q: 3. Fxz²i + (1 - 3xy)j + yzk, A. xyi + 2yzj - 3yk B. zi + 2xzj - 3yk C. zi + 2zj3xk D. xi + 2yzj-3yk…

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Q: Find the inverse Laplace transform of the function G(s) = as + b s² +82 .a = = 4, b=9, ß = 9.

A: We have to find the inverse Laplace transform of the function  G(s)=as+bs2+β2.a where a=4 , b=9 ,β=9…

Q: Evaluate. [5x-31 X dx

A: To evaluate the integration of (5x-3)/(x^2-x)

Q: Prove that if n is an integer and n³ + 5 is odd, then n is even using a) A proof by contraposition.…

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Q: Find the unit tangent vector of the given curve. r(t) = (7t cost-7 sin t)j + (7t sint + 7 cos t) k…

A: The given question is related with unit tangent vector. Given that,               rt = 7t cost - 7…

Q: Determine the radius and height of the largest cylinder that can be inscribed in a cone of the…

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Q: What are the edges incident on v2? (b) What are the vertices adjacent to v2 ? (c) What are the…

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Q: • Evaluat the integral:- 푼 S S. seč (cosx) dx dy Sin y

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Q: . What is the coefficient of ?^4 when (3+4x^2)^3 is expanded?

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Q: The height in feet of a seat on a Ferris wheel is given by the function h(t) = 50 sin (2πt/10) + 60.…

A: The height of the Ferris wheel is given by the below function. ht=50sin2πt10+60

Q: 9. Use the Residues Theorem to calculate 1+ sin² ª -de. Sketch the contour you used.

A: We have to find integral using Residue Theorem.

Q: Test the series for convergence or divergence using the Alternating Series Test. (-1)^-1 4 + 7n n=1…

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Q: Use the logistic growth model to predict the population of a species after three years given the…

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Q: In a mid-size company, the distribution of the number of phone calls answered each day by each of…

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Q: 1 Р ven as If th ● q 2 x are real and positiv llowing relations shc

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Q: 16-20 INITIAL VALUE PROBLEMS Solve the given problem. (Show the details.) 16. "2" + 4y' - 8y = 0,…

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Q: Ques.4 Decomposition 3z = 14 Solve the system of three simultaneous linear equations by using Crout…

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Q: 8. Prove that the differential operator M: C² [a,b] → C[a,b] defined by d²u du Mu= 2+3u dx is a…

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Q: Use an argument using Taylor series to evaluate: (a) 1 1 + - - + 2 3 4 Note: Find the Taylor series…

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