Find the average value of f(x) = 2 sin²(x) over [0, 2π].

Q: Suppose that the monthly marginal cost for firefighting portable water tanks is C'(x) = 2.5x + 115…

A: NOTE: Refresh your page if you can't see any equations. . the marginal cost function is

Q: 3.) [₁ y(2y² +1)* dy

A: To evaluate the given integral

Q: lim (2-4)³-8 lim it-4

A:

Q: Let f(x) = 4√√x+5x. Verify that f(x) satisfies the conditions of Mean Value Theorem on the interval…

A: Here is the solution:

Q: Find the rate of change of total revenue, cost, and profit with respect to time. Assume that R(x)…

A: To find the rate of change of total revenue, cost, and profit with respect to time. Assume that Rx…

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A: we need to solve the given initial value problem.

Q: Determine if the limit 4 x + 1 X lim x 0 exists, and if it does, find its value. 1. limit = 5 2.…

A:

Q: Determine the domain of the function of two variables f(x,y)=√y + 5x. The domain is {(x,y) (Type an…

A: The given function fx,y=y+5x. We have to find its domain.

Q: Write the complex number 7 - n(0)), with r> 0,0 ≤0 ≤ 2. 6ż in polar form, r(cos(0) + i sin(

A:

Q: Given the information below, define a set of parametric equations, x(t) and y(t) to model the…

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Q: Which equation below best represents the equation of a sine function with the given characteristics?…

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Q: Use sigma notation to write the sum. 1 5(4) Σ i = 1 + 2 5(5) + 3 5(6) + + 10 5(13)

A:

Q: 8. Find the differential of each function: (a)y=tan(cos.x) : (b) y=- Answer D

A: 8) a) y= tan(cosx)

Q: Consider f(x) = |x − 3| on [0, 5]. Find all c so that f(c) = fave where fave is the average value of…

A:

Q: Find the following antiderivative. J dx (x ln x) In (In a

A: To evaluate the antiderivative

Q: A car rental company charges 40 dollars per day, 15 cents per kilometre driven, and a 30 dollar…

A: we know that   10 cents=$0.1given  per day charge is  $4015 cents per kilometer driven $30 for one…

Q: Using identities to simplify completely trigonometric expression below :  sec t / tan t    *I…

A:

Q: The velocity of a body is given by v(t) = 2t, 1≤t≤5        = 5t2 + 3, 5<t≤14 where t is in…

A: Given function:- vt=2t1≤t≤55t2+35&lt;t≤14

Q: Find the distance from the point (6,-5,-4) to the yz-plane

A: Given point (6,-5,-4)

Q: Answer the following questions about the function whose derivative is given below. a. What are the…

A: To solve the following problem and find critical points, maximum, minimum points.

Q: b) Suppose that w = x2 + y² - z2 and_x = p sin + cos0, y = p sin ф sin 0 , z = p cos ф Əw aw find…

A:

Q: Find the particular solution for the initial value problem. dy + 4x³ = 6x² and y=2 when x = 0 dx y=0

A:

Q: Write an integral in the form A = increases from 5 units to 12 units. Evaluate the integral to find…

A:

Q: Calculate the limit algebraically. (If an answer does not exist, enter DNE.) x6 + 6,000x³ +…

A:

Q: Find the equation for the parabola that has its focus at (−35/4,−3) and has directrix x=-29/4.

A:

Q: Verify that the hypotheses of the Mean-Value Theorem are satisfied on the given interval and find…

A:

Q: Your company determines that the marginal cost, C', of producing the xth unit is given by the…

A:

Q: Let f(x) = 3x + 3 and g(x) = 4x² + 2x. After simplifying, (fg)(x) = 12x2 + 6x +3 X

A: NOTE: Refresh your page if you can't see any equations. . here we have

Q: Suppose f(x, y) = x²y + 6. Compute the following quantities: f(0, 0) f(4, -3) • f(-3, 4) . . = =…

A: NOTE: Refresh your page if you can't see any equations. . substitute (x,y)=(0,0)

Q: 3. A farmer has a plot of land bordering an extremely straight river bank. The farmer wants to…

A: NOTE: Refresh your page if you can't see any equations. . x=width of the rectangular plot y=length…

Q: Solve for the variable in each equation below. Gi (a) log(y 1) + log(y + 1) = log 8 -

A: Since you have asked multiple question, we will solve the first question for you as per our guide…

Q: 1) 2² Evaluate ze x² + y² + 2 dv where E is the portion of the ball x² + y² + z² = 1 that is in the…

A:

Q: Find the curve in the xy-plane that passes through the point (4,6) and whose slope at each point is…

A:

Q: Substition Simple Ing (x + Iny) dx = (x²) dy-0 III Solve using

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Q: A clothing company determines that its marginal cost, in dollars per dress, is given by the funtion…

A: NOTE: Refresh your page if you can't see any equations. . the marginal cost function is  where…

Q: = Farmer Jones, and his wife, Dr. Jones, decide to build a fence in their field, to keep the sheep…

A:

Q: Let F = . Calculate the divergence of F and - - find point P where div(F) = 0. P=

A:

Q: Evaluate 1. limit 2. limit = -3 3. limit does not exist 4. limit x+1 lim x⇒−1 x² – 3x − 4˚ 1 5.…

A: Given: limx→-1x+1x2-3x-4

Q: How do you measure distance along a smooth curve in space from a preselected base point? Give an…

A: To find: measure distance along a smooth curve in space from a preselected base point

Q: -45 + 7(x + 2) - 6x (no justification needed) = -45+ (7x + 14) - 6x = -45+ (14 + 7x) - 6x = (-45 +…

A: Part 2 Given that , -45+7x+2-6x For each step, use a property of the real numbers.

Q: Find the exact slope of the tangent line to the 5 cos(t) 2 sin(t) parametric curve t co/= 3 X { y =…

A: slope is  dydxdydx=dydtdxdtdsintdt=costdcostdt=-sint

Q: Check the convergence or divergence of the following series and find the sum if the series converges

A: We have to find if the given series converges.

Q: Find the function y(x) satisfying dy - 12/13 = 8x and y(-1)= -6. dy - 12/13 The function y(x)…

A:

Q: Suppose that C = f(x, t) = 22te-(6-2)t represents the concentration (in mg/liter) of a drug in the…

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Q: (-2,2 y=x+4 (3,7) y=x²-2 X

A: Given query is to find the area of the shaded region.

Q: The point of intersection between these two lines 2x + y = 4 x + 3y = 7  is  ....

A: Given the equations are  2x+y = 4 ......... (1)  X+3y = 7 ...........(2) Multiply the equation (2) *…

Q: Evaluate the geometric series or state that it diverges. 8 Σe-2n n=0 Select the correct choice below…

A: Given sereis:- ∑n=0∞e-2n

Q: (+/- 4√x²) dx 2x³

A:

Q: Find the indicated partial derivatives of: дz дх Oz au || || Z= 4x x2+y2

A:

Q: Eliminate the parameter t to find a simplified Cartesian equation of the form y = mx + b for ſ x(t)…

A: