H/F.. F. dr, where C is given by the vector function r(t) Evaluate the line integral F(x, y, z) = (x + y)i + (y - z)j + z²k r(t) = t² i + t³j+t² k, 0≤ t ≤ 1

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A: x=t3-3t    y=t2-2 To determine horizontal and vertical tangent    dydx=dydtdxdt…

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Q: Differentiate the following function with respect to x, fully simplifying the answer: y = 3 sin(2x)…

A: given y=3sin(2x)5cos(4x)

Q: [3] Solve the differential equation dy-6% +8y-cos³x. de

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Q: Find the derivative of the following function. 5. f(x) = - cosh *3x

A: The given function is ƒ(x) = - cosh5(3x)

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Q: Find the sum of the first six terms of the geometric sequence: - 5, - 15, - 45, . . .

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Q: Find dy dy dx X = sin2(0), y cos cos² (0)

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Q: Use the rules for sums of powers of integers to compute the sum. k Submit Question Jump to Answer

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Q: Use the quotient rule to find the derivative of 4x² + 2 k(x) 6x - 2 =

A: We know that the quotient rules of the d/dx(u/v)=(v*du/dx-u*dv/dx)/v^2

Q: 320(1.6)* for x using logs. x =

A: We need to find value of x.

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Q: Find the complex zeros of the following polynomial function. Write f in factored form. f(x)=x² + x³…

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Q: Let F(x) F'(x) = 1.3 - 1.₁³. = x -4 tan(t) dt. Use the Fundamental Theorem of Calculus to find…

A: given,  F(x)=∫x1.3-4tan(t)dt

Q: Find or evaluate the integral by completing the square. (Remember to use absolute values where…

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Q: The rate of depreciation (in dollars per year) for a certain truck is given by the function below,…

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Q: Evaluate the definite integral. 8 0 1 4 3 3x + 13 X + 9 dx

A: Explanation and some important formulas::-

Q: 18 • Σ =1

A: let  G=∑k=118(k2)

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Q: Find the first three non-zero terms of the Maclaurin Series expansion for the function, f(=)…

A: For ln(1 - 6x), we have: f(x) = ln(1 - 6x) f'(x) = -6/(1 - 6x) f''(x) = 36/(1 - 6x)^2 f'''(x) =…

Q: Find the indefinite integral. (Use C for the constant of integration.) [x²³(4x² + 4x4 + 1)⁹ dx

A: Given integral ∫x3( 4x4 + 1 )9dx Formula used ∫xndx = xn+1n+1 + C

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Q: 45. 2x + 3y = 6 X- 1 2 46. 1 (+2 x + y = -2 x - 2y = 8

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Q: Find dx dy dx 11 x = √√t, y = 7-t

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Q: Suppose a product's revenue function is given by R(q) = −8q² + 200q. Find an expression for the…

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Q: A juice company has found that the marginal cost of producing x pints of fresh-squeezed orange juice…

A: The left Riemann sum∫abf(x)dx≈∆x(f(x0)+f(x1)+f(x2)+⋯+f(xn-2)+f(xn-1))∆x=b-an

Q: f(x, y) = Ax² - Bxy + Cy² + x - y

A: f(x, y) = Ax2 - Bxy + Cy2 + x - y A = 4B = 4C = 2X0 = (x0, y0) = (5, 6) α = 1

Q: has two solutions. The smaller is 22x5×2x+6=0 and the larger is

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Q: Determine whether or not the vector field is conservative. If it is conservative, find a function f…

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Q: Use the figures to calculate the left and right Riemann sums for f on the given interval and the…

A: Solution: Given function, f(x)= 3/x + 1 ,[1,5] n =4

Q: Σ²n=0 n(x+2)" ΠΞΟ 3n+1

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Q: We know that a= 23 sin' (ax) cos(ax) dx = sin³ (ax) b Find b + C

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Q: Find the derivative of the function. y = x²ex - 2xex + 5ex y' = x² et + 3et 2

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Q: A population of squirrels in a forest is observed to be 190 squirrels at time t = 0. After a month,…

A: We have to find P(t) and predict the population size after 2 years.

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Q: Let J = 31 +43 - K and ✓ = 2₁ +3₁-2k be of two vectors. Find the component and projection U in the…

A: u→=3i+4j-k,v→=2i+3j-2k

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Q: a. Find the Jacobian of the transformation x = 2u, y = 4uv and sketch the region G: 2 ≤2u≤ 4, 4 ≤…

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Q: 32 Determine the maximum and minimum values of the function f(x) = 2x+² on the interval -2≤x≤8.

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Q: . Find the volume above the paraboloid z = x² + y² and below the cone z = √x² + y².

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Q: Find the most general antiderivative for the function Antiderivative = + 6 - 4√√x².

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Q: Let f(x) = 5x 752033 Then f'(x) And written as a decimal to three decimal places, ƒ'( − 4) = =

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Q: Find the area of the region that lies inside both curves r = 2 sin(20), r= 2 sin(0) 0 Area =

A: Area in the polar region is given by A = 12∫r2dθ Given function  r = 2sin( 2θ ) r = 2sinθ