If xy2 3x2y + C, then what is the value of C at (2,2)?

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Q: Evaluate the definite integral. sin(3t)dt

A: I=∫0π3 sin(3t) dt  =-cos(3t)30π3  =-13 cos3π3-cos0

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A: We will find if this is exponential.

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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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Q: 7- Differentiate K(x)=(Vx)(5x²+1)³

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A: For critical points first derivative must be zero If second derivative is less than zero then local…

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

A: Use the parameterization of curve for finding the length of curve .

Q: Assuming that a DE has a general solution a+y= 3r +C, what is the particular solution at given the…

A: Explained below

Q: A street light is mounted at the top of a 15 ft tall pole. A man 6 ft tall walks away from the pole…

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Q: Evaluate the indefinite integral. .3 6 + x*dx

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Q: Sketch the region enclosed by Y 6x and y = 9x". Find the area of the region.

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Q: Determine the value of b:

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Q: Consider the region R shown in the following figure, which involves the curves of equations 72 x2 +…

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Q: 15r If F(r) = and o is the surface (r – 3)? + y +z? = 49 oriented outwards, what is the value of F n…

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Q: x2 dr. Væ + 2 1. Evaluate -1

A: Integrate by parts.

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Q: r(t) = cos(Tt)i – In(t)j+ vt – 16k; to = 17 %3D Choose one▼

A: Given

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

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Q: Use part I of the Fundamental Theorem of Calculus to find the derivative of 15 f(x): dt f'(x) -…

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Q: Use the formula for the sum of a geometric series to find the sum or state that the series diverges.…

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Q: Consider the curve parameterized by x 3t2 15 and y 2t 15. Find equations for all tangent lines to…

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Q: Consider the function f(x) = 6x² – 2x + 11, 0 < x < 6. The absolute maximum of f(x) (on the given…

A: This question can be solved using the concept of absolute maxima and absolute minima.

Q: Find the exact length of the curve given by a = t° ,y (0 <t< 4). Length =

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Q: Describe the graph of the equation x2 + 4x – 16y + 36 = 0. -

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Q: Solve the following differential equations of dy 1 y= xy': + dx

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Q: Mark the critical points on the following graph. 교e-등, 98 980+ 882 784 686 588 490 392 294 196 98

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Q: Kuya Bill is selling 'Bill phones'. If the cost for selling r phones is given by 10000 C(r) = 120x +…

A: Given, Cost function, C(x) = 120x + 10000/x - 2000 Price Dand function, p(x) = 1000 - 2000/x2 + 200x

Q: Use Stokes' Theorem to evaluate F- dr. F(x, y, z) = xyi + x*j+z?k where Cis the intersection of the…

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Q: Let y = 5x?. Find the change in y, Ay when x = 2 and Ar 0.4 Find the differential dy when a = 2 and…

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Q: Assume the annual rate of change in the national debt of a country (in billions of dollars per year)…

A: Solve for debt equation by integrating the given equation.

Q: 4. For the given function find the local extrema using the Second Derivative Test. f(x) = x³ – 9x2 +…

A: maxima minima

Q: Question 2 A balloon is rising vertically over a point A on the ground at the rate of 15 feet per…

A: Using differentiation

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Q: Sheldon is being chased back-and-forth by a dog along Euclid Avenue. His directed distance (in…

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Q: Match the vector field with its graph. F(x, y) = yi 6. -6+ y 十H HH

A: We need to match vector field with its graph.

Q: Find ke ende finite integral. cuse c for Ge Constant of entyration) J Sin 39 Jcos 34 de (the + are…

A: We need to solve integral.

Q: Evaluate the line integral along the path C given by x = 2t, y = 8t, where 0 sts 1. 3у?) dy

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Q: 3 Find the area of the region bounded by the following:

A: Given r^2=2cos(2θ) , r=1

Q: f(x) = 2 – 5x², - 5< x < 1.

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Q: Find all the values of x where the tangent line to the function f(x) = x° - 8x - 6x +2 is…

A: For horizontal tangent line dydx=0 Given :

Q: Find the probability that a randomly selected value of X lies in the interval [3, 5] if f(x) 1 - x².…

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Q: The function f(x) = 2+ 6x + 150x- has one local minimum and one local maximum. This function has a…

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Q: Use the log rule of differentiation and differentiate y with respect to x.  y = ln( 8 + ex 8 − ex

A: given function