Find the average value of f(x) = Vĩ on the interval [0, 25]. favg %3D Enter your answer as a fraction.

Q: by L'Hopital's rule 1-cos(x) lim x2

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Q: Let fx) = 10x +4-15 ex, Then the equation of the tangent line to the graph of fa) at the point (0,-1...

A: I am attaching image so that you understand each and every step.

Q: 2. In 3-space the distance d from a point P to the line L through points A and B can be expressed as...

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Q: case

A: We will find the type of equation and draw the graph. 

Q: Given: 1. v = 2i – 4j + v5 k, u = -2i + 4j – V5 k 2. v =i+k, u = 5i + 12j | 3 4 Find: a. u· v, |v|, ...

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Q: A tank in the shape of an inverted right circular cone has height 9 meters and radius 19 meters. It ...

A: Solution: Given, In an inverted cone-shaped tank, Height = 9 m and radius =19m The chocolate height ...

Q: If log, æ = 0.63, log, y = 1.46, and log, z = 1.77, loga

A: As we know that, The logarithmic properties: 1). logaxb=b·logax 2). logaxy=logax+logay 2). logaxy=lo...

Q: 1-cos(x) lim x→0

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Q: The price p (in dollars per pound) and demand x (in pounds) for almonds are related by x = 5600 ln(1...

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Q: Find f'(x) if f(x)= 5sin^2(4x^2-5x+1)

A: Question- Find f'(x) if f(x)= 5sin^2(4x^2-5x+1)

Q: S sin 3xcos"3xdd

A: Given: ∫sin43xcos43xdx Let I=∫sin43xcos43xdx  ⇒I=116∫2sin3xcos3x4dx ⇒I=116∫sin46xdx

Q: Evaluate the integral Sr 8ry dA, where Ris the triangle 8x + y 0, y > 0.

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Q: Find the general solution of the equation: у" - у' - бу %3Dexp(-x) - 7 сosx

A: Given : y"-y'-6y=exp(-x)-7cosx

Q: Solve this differential equation: dy 0.03(700 – y) dt y(0) = 45 y(t) =

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Q: find the second derivative of y=[(tane^3x)+(e^tan3x)]

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Q: Evaluate L- {; 3s+1 s2+6s+13

A: L-13s+1s2+6s+13

Q: 1. S 5e* dx 2. S(2 – 3e*) dx 3. S 72x+3 dx 4. S dx x In x 3 dy 5. S 4y-3 6. S dx 2 x+5 7. Se* (1 + 2...

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Q: What are the 5th roots of -1? Show complete solution

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Q: Directions Show the following x-6xt3 is continuour on the in terval [-8,2]. |

A: To show that the given function is continuous in the interval [-3,2]

Q: Let u = (-3,4) and v = (2, –5). Find (a) the component form of the vector 3u – 4v and (b) its magnit...

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Q: 5.S dx 2 x+5

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Q: Find the area bounded by the curve y = x2, AB is tangent to this curve at point P (2,4) and the x- a...

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Q: Determine the force in members CD, CJ, KJ of the truss which serves to support the deck of a bridge....

A: Taking assumptions Forces away from joint is Tension (+)  Forces towards joint is compression (-)  I...

Q: Find the area of the triangle with vertices P(1,5, –2), Q(0,0,0) and R(3,4, 1). NOTE: Enter the exac...

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Q: Parametric equations for the line through (5,3, 7) and parallel to the line r = 3 – t, y = 2, 2 = 8+...

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Q: Use implicit differentiation to find y' and then evaluate y' at (-2,1). xS + 32y = In y %3D y'l(-2,1...

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Q: sinh x + cosh x)ª= e4x

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Q: Use Cramer's rule to solve the system of equations. If D = 0, use another method to determine the so...

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Q: 7 dx x + 1 -1

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Q: Vx +1- 1 1. Determine whether the function f defined by f(x) is continuous or discontinuos at a = 0....

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Q: x'- x - 3x - 2 dx 4 x* - x' + 4x- 4x .3 |

A: To find out the integration of the function given. 

Q: Question 2 Find the domain: X-y f (x.y) = x2+x-6 O {(x, y): x# -3 and x # 2} O (x, y): x - y 0} O En...

A: The function should be well defined. For this function to be well defined, denominator must not be e...

Q: Directions: Evaluate the following integrals. Show your complete solutions. Identify the u and the d...

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Q: Parametric equations for the line through (5, 3, 7) and parallel to the line æ = 3 – t, y = 2, z = 8...

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Q: for a particular commodity, the demand function is q= 1/4(400-p^3). fine e when p=6

A: To find e when p=6

Q: Find the laplace transform of f(t)= { t 02

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Q: Solve the given initial-value problem. (Use x as the independent variable.) 2y'y" = 1, y(0) = 2, y'(...

A: Here we have to solve the given initial-value problem.    2y'y"=1 , y(0)=2 , y'(0)=1 

Q: 3. Use the Comparison Test to determine if the series 5n Cos 2n n3 + n2 +1 n=1 converges or diverges...

A: Using P and comparison test. 

Q: find the fur pose of the function- and give the reason. メ * x²4+ 3× メ<t

A: Follow the procedure given below.

Q: 2. y(x? + y? – 1)dx + x(x² + y² + 1)dy = 0

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Q: estion 7 Find an equation of the plane containing the points A=(1,0,2), B = (-1,1,2), C= (5,0,3). Fo...

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Q: An engineer and his helper can do a certain job in 5 hrs. On a given day, they work together for 2 h...

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Q: (a) Using Gaussian elimination, find a vector v such that

A: As per our guideline is multiple questions are posted we are supposed to answer only the first one. ...

Q: 4[xn+f(xn=1)] p'(xn-4) criterion is x 0.102.

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Q: at x = The function has a relative minimum of at x = The function is increasing on the interval(s):

A: Since you have asked multiple part question, we will solve the first 3 part of the question for you ...

Q: The cost of producing a car depends on the price of steel (s) in dollars per pound and the hourly wa...

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Q: 1. Find the local maximum and minimum values and saddle point(s) of the function. If you have three-...

A: Given

Q: Sand being dumped from a fannel forms a Conical Pile whose height is always 13 the diameter of the b...

A: volume of cone

Q: 3) A cylindrical fish tank is 8 meters deep and has a radius of 3 meters. The depth of water in the ...

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Q: find (y') by Implicit differentiation x² tan(y) + y10 sec(x) = 2x

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