Use a product-to-sum formula to convert the expression to a sum or difference. Simplify where possible. sin 3t cos (s - t)

Q: Use the divergence theorem to find the outward flux of F across the boundary of the region D.…

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Q: Evaluate the integral by reversing the order of integration. y cos(x²) dady = -0.072

A: To evaluate the following integral by reversing the order of integration.

Q: Can this also be done by comparing 2 normal vectors? Why or why not?

A: The given equation of line  and equation of plane

Q: Consider the function f(t) = 9 sec² (t) — 6t³. Let F(t) be the antiderivative of f(t) with F(0) = 0.…

A: Given, f(t) = 9 sec2(t) - 6t3 F(t) is the antiderivative of f(t) F(0) =0 Find, F(5)

Q: Use Green's Theorem to find the counterclockwise circulation and outward flux for the field F = (2y²…

A: The given vector function  and curve C: the triangle bounded by The circulation of a vector field is…

Q: Find the radius of convergence and the interval of convergence of the series. n=1 8n-1

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Q: An airplane is heading east with an airspeed of 300 km/h. The plane encounters a wind from the west…

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Q: d) lim √x²+x-3 - 2x

A: given limit

Q: Pls help ASAP and pls provide all steps and calculations

A: Consider the graph

Q: Consider the following series, Σ(-1) ¹-1x n=1 (a) Find the radius of convergence, R, of the series.…

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Q: -10 (-2, 196) -8 -6 (-4.5,-54) 4 2 A f(x)=4x³-8x²-70x+108 B f(x)=4x³-6x²-72x+108 C…

A: The given graph

Q: The integral in this exercise converges. Evaluate the integral without using a table ∞ 00 1-2 dx B…

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Q: limx→0 limx→1 log(1+x) X log x 1 – x

A: We know the expansion of log(1+x) is: log(1+x)= x -x2/2 +x3/3 -x4/4+......

Q: Find the indefinite integral. Check your result by differentiating. (Use C for the constant of…

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Q: The total cost function for a product is C(x) = 875 ln(x + 10) + 1900, where is the number of items…

A: The total cost function for a product is where x is the number of items produced.(a) To find the…

Q: Find the area between y = 1 and y = (x − 1)² – 3 with x ≥ 0 - Q The area between the curves is…

A: Consider the graph

Q: Convert the following equation to Cartesian coordinates. Describe the resulting curve. r= -2 cos…

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Q: The velocity of an object is given by, V ds dt = u + at where, u is the initial velocity, a is the…

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Q: hate the following definite in 0 π sin5x dx

A: According to our guidelines, we are supposed to answer only one question if multiple questions are…

Q: Simplify 0.5+ log 9 + {(ln15 - ln3)/ (ln75 - In3)} – In9/ln10 Substitution)

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Q: Divergence and Curl Let F = ⟨2xyz, 3y^2 z, 4x^2 y⟩. (a) Compute div F. (b) Compute curl F. (c)…

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Q: Find the centroid of the region lying underneath the graph of the function over the given interval.…

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Q: 1. Evaluate the following definite integrals: √₁²x² (x³ + 1)³ dx B b. dx 3x² dx

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Q: Problem 5. Find the arc-length distance of the curve from t = - In 4 to t = 0? r(t) = (e cost)i +…

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Q: n Suppose that p(x) = ► anx converges on (-1, 1], find 'n' n=0 the interval of convergence of p(7x -…

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Q: Find the curl of the vector field ♬ =. curl F = j+ 12 k

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Q: Find all holes of the following function. If a hole exists, write your answer as a coordinate point…

A: The given function .The aim is to find the holes in the function.

Q: 9) Analyze the function f(x)=(x+1)e*. Report extrema, inflection points, intervals of monotonicity…

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Q: Determine wheter the sequence converges or diverges if converges, find the limits. an = 9+ (-1) " 9

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Q: Compute the value of the improper integral. (If the integral diverges to ∞, type oo; if the integral…

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Q: A company makes portable heaters for outdoor dining. The company has total cost function C(x) =…

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Q: Directions: Use the digits 1 to 9, at most one time each, to fill in the boxes so that the line is…

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Q: Separate the variables and solve the differential equation. dy/dx =(((3x^2)+1)/(4y)) ;   y(0)=2

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Q: Given the series: 1 1 1+ + + 5 25 1 125 + does this series converge or diverge? converges diverges…

A: Consider the series

Q: A projectile is fired vertically upward into the air, its position (in feet) above the ground after…

A: A projectile is fired vertically upward into the air, its position (in feet) above the ground after…

Q: Use the Ratio Test to determine if the following series converges absolutely or diverges. 8 Σ (−1)n…

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Q: Consider the following indefinite integral. The integrand decomposes into the form: Compute the…

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Q: Investigate the following functions for Local Maximum and Local minimum point. 1) F(x, y, ²) = x² +…

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Q: a. Find the derivative function f for the function f. b. Find an equation of the line tangent to the…

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Q: 1) Consider the function f defined piecewise. x < 2 f(x)= x³ +1₂ [x² + bx₂ x ≥2 a) Isf continuous at…

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Q: 2π 1²t S (лx + sin x) dx (πχ π

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Q: After we apply the Laplace transform to the equation y"-2y'+2y=e', given the initial condition y (0)…

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Q: Evaluate the following limit. Use l'Hôpital's Rule when it is convenient and applicable. lim (→ lim…

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Q: 38. Given two lines, determine if the lines intersect, if the lines are parallel, or if they are…

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Q: Find the derivative of y with respect to z. y = In (cosh 3z) y' =

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Q: Solve the following problem and show your complete solutions. Explain your answer for better…

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Q: = y(x) (for x > 0) which satisfies the separable differential equatic x > 0 with the initial…

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Q: Water is leaking out of an inverted conical tank at a rate of 14900 cubic centimeters per min at the…

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Q: Find (a). the square roots of z = 5 + 12i (b). the 8th roots of unity.

A: We have to find the square roots of z = 5 + 12i and the 8th roots of unity.

Q: product of the vectors u and v, and find the angle between the vectors. and v= (1,3,5). f the…

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