Find the curvature and radius of curvature of the plane curve at the given value of x. y = e−x/2,  x = 4

Q: Determine whether Rolle's Theorem can be applied to f on the closed interval [a, b]. (Select all…

A: See this solution in below.

Q: Find a vector function that represents the curves of intersection of the two surfaces. 1.- The…

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Q: The ordering and transportation cost C for components used in a manufacturing process is…

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Q: Q2: Fill in the blanks : 1- ff f(x,y)dydx represents the. 2- y" +(3y')5 - sinx = 4 of order 3-ye…

A: Since multiple questions are asked I am answering first 3 subparts

Q: explain

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Q: For the next three exercises, use series to evaluate the limit. arctan y - sin y y³ cos y 2 lim h-0…

A: Disclaimer: Since you have posted a question with multiple sub-parts ,we will solve first three…

Q: Find the relative rate of change. Evaluate the relative rate of change at the given value(s) of t. -…

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Q: (a) Find the integral of 6.x8 √21° +7 dx. **IDENTIA YAMIMATIO

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Q: What prevents the transformation (x,y)=(3x, -3y) from being called a dilation? Explain your awnser.

A: Given (x,y)=(3x,-3y) Dilation is a transformation, which is used to resize the object.

Q: Evaluate the following limit. Use l'Hôpital's Rule when it is convenient and applicable.   lim x→∞…

A: The given limit,      limx→∞1+axx, for some constant 'a'

Q: -S 3x²-6x+7 x3-x²-x+1 dx

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

Q: The differential equation 2ydx-(3y-2x)dy=0 is Exact homogenous and linear O

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Q: Solve the equation. dx 2x1² dt **** An implicit solution in the form F(t, x) = C is =C, where C is…

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Q: You have 100 feet of fencing to build a pen in the shape of a circular sector, the "pie slice"…

A: Given the perimeter of the circular sector is 100 feet   i.e. r+r+s = 100   ⇒ 2r+s = 100    ⇒ s =…

Q: Solve the initial value problem y" + 5y' - 24y = 0, y(0) = a, y'(0) = 80. Find a so that the…

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Q: Find the general solution of the following differential equation. 81y" - 4y = 0 NOTE: Use c₁ and ca…

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Q: S cos 2x dx COSX

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Q: Using Rolle's theorem for the following function, find all values c in the given interval where…

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Q: B: if Z-4x²-8xy +7y5-3 then find Z, Zy, Zxx, Zyy

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Q: if f(x,y) = √x² + y + 4, then find a a21 and ах ду х

A: If fx, y=x2+y+4, then to find ∂2f∂x2 and ∂2f∂y∂x.

Q: Question 2 Given the equation -5x² + 30x - 5y2 - 10y - 5z2 - 90z – 5z² 90z = 210 a) Show that the…

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Q: * Convert the polar equation to rectangular form r=7 (solve) x² + y² = 7 x=7 O Option 4 x² + y² = 49…

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Q: Evaluate the indefinite integral. x² A -dx 1- x6

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Q: A container manufacturer plans to make rectangular boxes whose bottom and top measure x by 3x. The…

A: We need to find height.

Q: Solve DU 11 dx 4x+3 x³ +2x² + x

A: ∫4x+3x3+2x2+xdx=∫3x-3x+1+1x+12dx=∫3xdx-∫3x+1dx+∫1x+12dx=3lnx-3lnx+1-1x+1Add a constant to the…

Q: approximation with 5 subdivisions. 3 2 1 2 3 4 5 6 7 P∞ot 8

A: solution is given below

Q: Integrate (sinx + cos^2x)^3 dx

A: To evaluate: ∫sinx + cos2x3dx Let I = ∫sinx + cos2x3dx ⇒I =…

Q: y = f(x) = 8x² - 4x + 5 (a) Find the differential of f. dy = (b) Use your result from part (a) to…

A: Follow the procedure given below.

Q: In a pool filled with water to a depth of 1 Rectangular plate calculate the fluid force on one side…

A: Given: Depth of pool = 10ft Area of rectangular plate, A = 3ft×4ft=12 ft2  Hydrostatic Force on…

Q: Approximate the area under the curve y = x² from a = 3 to x = 6 using a Right Endpoint approximation…

A: Follow the procedure given below.

Q: Given the curve of y=6-x² and y=x+4. Sketch the graph for -3<x<3. State the intersection points…

A: We can find the area of the bounded by the given curves.

Q: Problem 7 Proof that if lim f(x) exists then it must be unique i.e., x→a if lim f(x) = L and lim…

A: In this question, we want to prove that if a limit of a function exist then it must be unique.

Q: This is the approximate time right ? Making the no. of days from feb to aug into 30, by that logic…

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Q: Represent the function CO = Compute the first few coefficients of this power series: C1 = C2 || C3 =…

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Q: If 4x² - y² = 64, show that ds² = 1/2 (15x² (5x² - 16) dx².

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Q: A particle in R2 has a velocity function of v(t) = (3t²-4, 6t + 2) (given in m/s). After moving for…

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Q: Use the Midpoint Rule with n = 4 to approximate the integral. √x + 5dx = [Please enter your answer…

A: Here we have to use the midpoint rule

Q: 6. Ifw = f(x-y, y-x), then show that, ar + L = 0. dx ay

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Q: The distance from the point K(3, -2, 0) to the xz- plane is Select one: O-2 O √13 O 0 02 None of…

A: We need to find out the distance between the given point and xz plane.

Q: (a) [1 Show that the following equation represents a sphere, and find its center and radius. x² + y²…

A: As per our guidelines we only solve one question and rest of the question will be reposted.

Q: y=x² from (0,0) to (1,1). | Compute the line integral of f(x)=2x over the curve 2009

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Q: The Taylor series expansion of 2 |z| < 1 is (solve) Z-2¹ −(¹ + ² + ² + ² …..) X Option 2 O…

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Q: If v=3i+2j+ k,w=3i+ 4k and the angle between v and w is 90, find v.w (solve) 10 8 0 O Option 3 O

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Q: x²5 - - 5y = x + 1 is non-homogeneous second order differential equations dy² with constant…

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Q: Evaluate the following expression. Your answer must be in exact form: for example, type pi/6 for DNE…

A: We can find the answer as below.

Q: Calculate the area of the parametric surface given by: r(u, v) = 2 sin u cos vi + 2 sin u sin vj + 2…

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Q: Let a = . Find a unit vector in the direction of a

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Q: he transformation from Cartesian to plane coordinates in x-direction is given by x=rsine x=rcos20…

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Q: A furniture store sells 96 coffee tables per month at $1100 each. The owners estimate that for each…

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Q: Evaluate 3 [²^{²} + √x² − ² + ³x² − ²) dx = x None of them 21.466 2.1664 -2.1646 -21.664 21.664…

A: Given problem:-