please

Q: 30 25. 2 k(k – 2)(k + 2). - k=1

A: "Since you have asked multiple questions, we will solve first question for you. If you want any…

Q: Consider the planes x – 10y – 2z = 3 and 2x – y + z = -13. Find the following. 1. The cosine of the…

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Q: b)Let f(x)=sinx. Calculate the arc length of the graph of f(x) over the interval [0,r]. Answer:

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Q: The equation of a line is given below. 4x+y=-1 Find the slope and the y-intercept. Then use them to…

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Q: 17. cos 2x + 3sin2x = 4 - 3sin?x %3D

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Q: 5.8 Evaluate n=1 2" -

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Q: 1. (a) Find a power series representation for f(x) %3D 1+ x3 (b) By differentiating the power series…

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Q: Please

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Q: Question 4 Rolle's theorem states that if a function fis continuous on the closed interval [a, b]…

A: Rolle's theorem states that if a function f is continuous on the closed interval [a, b] and…

Q: A. Using the definition of derivative, find the derivative of the follow function. 1) f(x) = ! 2)…

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Q: Sketch the region R under the curve y = 4x – x² above the x-axis from x = 1 to æ = 5. Use the…

A: Given problem:- Sketch the region R under the curve y = 4x - x2 above the x-axis from x=1 t x=5 Use…

Q: Set up a double integral in rectangular coordinates for calculating the volume of the solid under…

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Q: Section 1.5 In Exercises 1 and 2, we refer to a function f, but we do not provide its formula.…

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Q: Find the gradient of the function at the given point. f(x, y) = 4x + 3y2 + 6,    (1, 4) ∇f(1, 4) =

A: As we know that; The expression for the gradient vector; ∇fx,y=i∂∂x+j∂∂yfx,y=i∂fx,y∂x+j∂fx,y∂y…

Q: EXERCISES 2: Find all the local maxima, local minima, and saddle points of ti functions 1 f(x, y) =…

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Q: Use the Midpoint Rule with the given value of n to approximate the integral. Round the answer to…

A: Given that,     ∫210x3+1dx, n=4

Q: 8. Find the curvature of the plain curve y = e.

A: According to our guidelines, we can answer only one question. Other questions can be reposted.

Q: Given the power series En (n - 1) A, xla + 2) n =1 Use the technique that we covered in this lesson…

A: In this question we shift the index so that the exponent of the power series is simplified .  Note :…

Q: 2. Find the equation of the tangent line to the curve y = x2 - 2x -3 that is parallel to the line x…

A: Note: As per our guidelines we are supposed to answer only one question if there are multiple…

Q: Justify your answer whether the following functions are continuous or not at a certain point or…

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Q: Given the following limits, lim f(x) = 4, lim g(x) = 9, lim h(x) = 6, %3D %3D x→6 x→6 use the limit…

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Q: I3D Find the first partial derivatives of the following function. f(x,y)%3D3×Y

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Q: For eac. ation, determine whether it represents a direct variation, an inverse variation, or…

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Q: The sum of two positive numbers is 40. What are the numbers if their product is to be the largest. A…

A: let the two numbers be "x" and "y "x+y=40 → (1)F(x,y) = xyF(x)= x(40-x)F(x)=40x-x2differentiate…

Q: Divide. (-20x + 8x+ 5x* – 4– 3x) + (-5x - 3) Remainder Write your answer in the following form:…

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Q: If a > 0 and E 4, is convergente then Eola)" is also convergente Select one: O True OFalse if a, is…

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Q: Find the following derivatives. Z, and z,, where z= 6xy-5x y, x=s+t, and y =s-t %3D (Type an…

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Q: 7 n2+ 3 n+ 2 lim 7 9 n2+ 2 18 n- 00 Select one: O True O False

A: limn→∞7n2+3n+29n2+2

Q: Use Green's theorem to evaluate the line integral along the given positively oriented curve. | 8y dx…

A: Green's Theorem:- To find the line integral of a function along a closed curve C…

Q: b.) Use the pattern of successive differences to find the number of blocks in next L's. 1 4. 3 c.)…

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Q: Sketch a graph of the function f that is continuous on (- 00,00) and has the following properties.…

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Q: Divide. (22 + 11 - 20) - (,² +x =2) Remainder Write your answer in the following form: Quotient+ 2,…

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Q: The Mean Value Theorem states that if a function f is continuous on the closed interval [a,b] and…

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Q: y" – 2y +y = 0 %3D

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Q: continuous on the interval [-1,2), and is not differentiable on the interval (-1,2) urentiable on…

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Q: Write five other iterated integrals that are equal to S, L f(x,y,z)dz dx dy.

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Q: The area of the surface generated by revolving the curve y = y9 - x2,-2 < x < 2 about the x-axis is…

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Q: E 2na". n=0 Based on the Ratio Test, which of the following conditions on x will guarantee that the…

A: Ratio Test : Suppose we have the series ∑ an . Define,                         L = limn→∞…

Q: y=ln|sec3x + tan3x|

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Q: dy x +1 xy %3D dx

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Q: Evaluate the following limit. Use l'Hôpital's Rule when it is convenient and applicable. 4X-1 e lim…

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Q: tan² ydy 9. Find f tan² y+1 1 1 c.글y-3sin 2y + C D. y –sin2c + C A. y +sin 2 y + C 4 В. tan y — у +…

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Q: : Consider the differential equation y" – 2y – 3y = 5 cos(2x). a) Verify that the family of…

A: Given y(x)=c1e-x+c2e3x-713cos(2x)-413sin(2x)initial conditionsy(0)=-4 and y'(0)=4

Q: Find the tangent line for the level curve f(x,y) = 9x3y at the point (2,-8). a. -864x + 72y = -2304…

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Q: Find the area of the region enclosed by f(x) and the x-axis for the given function over the…

A: Use integration for finding the area under the given interval.

Q: 3- 3,9 dx

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Q: Let A be an eigenvalue of the n x n matrix A. Define A? to be the n x n matrix A? = AA. Show that X?…

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Q: Use polar coordinates to find the volume of the solid region that lies inside the sphere x2 + y2 +…

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Q: Let u be a differentiable function of r. Use the fact that |u| = Vu2 to prove that u'- u # 0. %3D dr

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Q: Given the power series Σ 4 (x - 3)" - n = 0 n + 2n Find the "Radius of Convergence" for the series.

A: Radius of convergence of the given power series  ∑n=0∞ 4n2+2nx-3n