Question 15 Find the work done by F over the curve in the direction of increasing t. F = Zi + -j + \k; C: r(t) = t³i+t5j + t³k, 0 st ≤ 1 y W 131 77 W = 17 O W=0 O W = 1

Q: (a) x= 3t — 4, y = 6t + 2 (b) x=2cos(t), y=5sin(t) (0 ≤t≤ 2π) (c) x= 2sin²(t), y = 3cos²(t) (0<t<7)

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Q: 500 Compute the average rate of change of the function, f(x) =x³+3x2 _ over the interval [5,10].

A: We have to find the average rate of change of the given function over the given interval.

Q: If the percent decrease is 25%, what is the common ratio?

A: Common Ratio The common ratio is defined as the amount between each number in a geometric sequence.…

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Q: The function g is differentiable, and the tangent line to the graph of y = g(x) at x = -4 is y = 5x…

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Q: Compute the length of the curve r(t) = = (2t, In(t), t²) over the interval 1 ≤ t ≤ 8. (Use symbolic…

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Q: Find the work done by F over the curve in the direction of increasing t. F = 1/x+12 i + j + 8 k;…

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Q: The graph of the derivative f'(t) of f(t) is shown. Compute the total change of f(t) over the given…

A: To compute f(t) we have to first find equation of f'(t) and then integrate it.

Q: Let g(x) = - for f(t) dt, where f is the function whose graph is shown. y f 0 1 3 6 (a) Use part one…

A: Step 1: Step 2:Step 3:Step 4:

Q: 3. Find the work done by F over the curve in the direction of increasing t. = (2,x, y) = (sin t, cos…

A: Write the vector field F=zi+xj+yk The equation of the curve. rt=sinti+costj+tk Differentiate…

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Q: Use a tangent plane to approximate the value of the following function at the point…

A: If the function is fx,y=arctanxy2-699 So, fxx,y=y21+xy2-6992fyx,y=2xy1+xy2-6992 Now,…