3. S- dx 1-sin'x

Q: x +1 Evaluate the given limit of lim if it exists. 2→-1 x4 – 1 O limit does not exist 4 O -1

A: We have to find the limit

Q: A golfer hits an errant tee shot that lands in the rough. A marker in the center of the fairway is…

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Q: Match the equation with its graph. x2 y2 z2 + = 1 9 9 16 4 -5

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Q: Consider the initial-value problem y" + 4y = 5 sin 3t, y(0) = 0, y' (0) = 3. %3D (a) Use the Laplace…

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Q: 1. 5x²+4x2-5 dx

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Q: Find the series radius and interval of convergence for what values of x does the series converge x"…

A: We need to find radius and interval of convergence.

Q: 2. Find the r educed echelon form of the fo A = 0 0 0 6 54 0 (714161 Show your working

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Q: sin(x) dx B. Evaluate the integral 1- sin? (x)

A: Our Aim is to evaluate the integral ∫sin (x)1-sin2 (x) dx

Q: 12 For the given function y 3 cos ( 0 2 state the following (show al Work) a) Amplitude b) Period c)…

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Q: 7. Į V1- xdx 8. ſ e2x dx

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Q: A blimp, suspended in the air at a height of 400 feet, lies directly over a line from a sports…

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Q: Evaluate the line integral, where C is the given curve. xy ds, C: x = t2, y = 2t, 0sts 3

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Q: 9. S (6eº+1)/½ eo 10. |(1 + 2x)³ dx

A: We can solve as follows

Q: A. Identify the given differential equati. as to the dependent variable, degree of the equation,…

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Q: Select the correct answer. Which hyperbola has both foci lying in the same quadrant? O A. (- 24)2 (y…

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Q: Express à = (3, 1, – 1) as B + Č, where B is parallel to the vector (1, 4, 2) and Č is perpendicular…

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Q: Find the area bounded by y = x + 4 and y = x2 - 2.

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Q: 1. (1 + y?)° dy 2. S sin x+cotx dx sin?x

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Q: Fnd the average value of the function over the glven Interval. (Round your answer to three dedmal…

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Q: Evaluate the integral sin(t)dt

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Q: proportional

A: We will solve the problem.

Q: A dietitian at a hospital once a patient to have a meal that is 64 g of protein, 44 g of…

A: We need to find How many servings of each food should be given to the patient.

Q: The displacement, s in feet, of a particle moving in a straight line is given by s = 5t2 – 6t + 14,…

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Q: If fex) x2 f'co) 19+ t? dt find f'c3) %3D

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Q: Find [r(t) · u(t)] and [r(t) × u(t)] in two different ways. dt dt r(t) = ti + 8t2j + t³k, _u(t) =…

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Q: (7 cos° t dt 2

A: ∫0π/2 cos9tdt ∫0π/2 cost(1-sin2t )4dt here lets substitute that sint = u du/dt = cost du = costdt…

Q: B. Find the interval of convergence of the power series and find the sum of the series as a…

A: Series convergence

Q: 2 ー (4-x²) dx -2

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Q: 5sin e Cose de Sin? o +3 Sine -4 2.

A: Solve the following

Q: Give the symmetric equations of the line l perpendicular to the plane T : 5x – 2y = z+4 and passing…

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Q: Solve using product rule d(uv) = u dv + v du: f(x) = (3x^2 – x + 4) (2x^2 – 1)

A: Our Aim is to solve the given function using the Product Rule where f(x)=(3x2-x+4)(2x2-1)

Q: chain rule to find given w = x² + 2y² + z² and x = cos (st), y = -2s lnt an 3s2 Vt.

A: We have to find out derivative

Q: 6. Find equations of the tangent line and the normal line to the curve y = 1+ x2 at the point (1,)…

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Q: 1. 2x2 + 4x + y = 0,y = 2x %D %3D

A: Given :

Q: C. Find the general solution of the given variable separable equation. 1. 2cosx cosy dx - 3Isin x…

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Q: (425 + 62?)dx Find -2

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Q: ニ。

A: Given query is to find the solution of the differential equation.

Q: 10 10 If f (x) dx=17 and f (x) dx=12, then f (x) dx=5 . 8. (A) True (B) False

A: To determine whether the given statement is true or false.

Q: (1) fx sin x dx

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Q: Find r'(t). r(t) = (tan(3t))i+t cos(t)j – Vēk NOTE: Enter your answer in terms of i, j, and k. r'(t)

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Q: e i+ - 1 (P-1)i-(e1-1)j+글 i - k

A: Given query is to find the integral.

Q: Find all the relative extrema and saddle points, if any, of the given function below: f(x, y) = In(x…

A: To find all the relative extrema and saddle points, if any, of the given function below:fx,…

Q: Problem 3: Given a function 4 - x2 g(x) = 3 - Vx2 + 5 Page 1 of 3 Use analytical method to determine…

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Q: Evaluate the following integrals. 2 (a) S(csce)(1 + sin´e + sine cot + sin¯0 + sin0 cot¯0 ´e)de

A: Solution is given below:

Q: Use the Fundamental Theorem of Calculus to find the "area under curve" of f() = 2x + 3 between x =…

A: Our Aim is to find the "area under curve"of f(x)=2x+3 between x=11 and x=13using the Fundamental…

Q: Find both first partial derivatives. z = 10y² Vx Oz dz %3D %3D

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Q: Find V x (V x F) if F(x, y, z) = 2:xy j+ 9xyz k. V x (V × F)

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Q: Find V x (V x F) If F(z,y.2) 10ryj+5zyzk. V x (V x F)

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Q: (8x + 4x)v4x² + 8 – 24x³ – 32x If f(x) = (/4x2 + 8 - x*) then f'(x) = 4r2 +8

A: f(x) = (4x2 +8 - x2 )2 f'(x) = (24x2 +8 - 2x2)(8x/(24x2 +8)  -2x ) f'(x) = ((24x2 +8 - 2x2)(4x -…

Q: 10 dx 5. S (10 +1)5 6. S 2r(e**+1 – 2**) dx

A: