/1 5/2 Find the length of the curve r (t) = ( t,4t,25t ) for 0

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A: This question can be solved using the concept of average value of a function in a given interval.

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A: Find out the maxima and minima.

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Q: Use properties of limits and algebraic methods to find the limit, if it exists. (If the limit is…

A: We can solve as follows

Q: Use the Derivative of the Inverse Theorem to calculate g'(x), where g is the inverse of f. f(x) x +…

A: Topic:- function and it's inverse function

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Q: Determine the following Laplace transforms: (i) mathcal L \ cos^ 2 3t\ .

A: Given

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Q: 8. If V represents the volume of an object, what does AP represent? - dt

A: dydx-Represent the Rate of change of 'y' with respect to 'x'. Here, 'y' is dependent variable and…

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Q: 3) Ernie the African Elephant is 9 feet tall and weighs 6 2 tons. Elijah is a similarly-shaped…

A: Unitary method: The unitary technique entails first determining the value of a single unit, followed…

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Q: 9) Determine the third derivative with respect to x for y = In x 10) Given f(x) 2x + 1 and f(1) 4.…

A: Find the derivative

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A: Using greens theorem

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Q: A bumblebee was released and started to travel along a straight horizontal line. The directed…

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Q: Find the arc length of the parametric curve. = 4 cos(t), y = 4 sin(t), z = 3t; 0<t<T %3D

A: Use arc length formula

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A: We have to choose correct option

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Q: 7- Differentiate K(x)=(Vx)(5x²+1)³

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Q: summation

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Q: Calculate the derivative. y = 2 cosh (x) coth (x) (Give an exact answer. Use symbolic notation and…

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Q: Q6. Identify the incorrect statement in the following: A. If e* = 2 then x = In 2. B. If In x = 2…

A: To find the incorrect statement we simply use basic properties of natural logarithm function.…

Q: if x 2 valuate each of the following, if it exists. (If an answer does not exist, enter DNE.) lim…

A: Solution of given question is written in below steps.

Q: r(t) = 4 cos(t)i+4sin(t)j; t = 3 /3 1 2/2' 2/2 -V3 2/2' 2/2 1

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Q: find the tangent plane to the surface z = y-x at the point (1,2,1)

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Q: Pierce Manufacturing determines that the daily revenue, in dollars, from the sale of x lawn chairs…

A: Here we will find all the quantities one by one,

Q: Find the derivative. ( cos ft dt x10 COS^/

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Q: The Trapezoidal Rule ou e id b oblw Jeot en f (x) dx = h +f(x1) + f(x2) + ..+ f(xn-1) +f(xn)) b-a…

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Q: dx 6x + x2

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Q: Given the Total Cost function, TC = 10 + 5Q?, find the marginal cost function, MC when Q = 10. [2]

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Q: Find the area of the region bounded by the curves x=y3 and y=x2.

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Q: Evaluate the line integral along the path C given by x = 2t, y = 8t, where U + dy

A: Given

Q: 1. Describe the graph of the equation: x2 – 5y2 – 4x – 10y – 46 = 0

A: Since you have posted multiple questions i can do first question as per our company guidelines…

Q: Find the Cartesian coordinates of the given point. (8, 0) 1) (0, 8) 2) (-8, 0) 3) (8, 0) 4) (0, -8)

A: Given problem:- Find the Cartesian coordinates of the given point.   (8,0)

Q: 8 Evaluate for (3x² -7x+4

A: We have to use the concept of derivatives

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Q: Determine whether the planes are parallel, perpendicular, or neither. 7x + 28y - 21z = 1, -3x + 6y +…

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Q: Let T: R - R be a linear transformation such that T(1, 1, 1) = (4, 0, -1), T(0, -1, 2) = (-5, 4,…

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