Evaluate the limits. Show your solutions. 1. lim lim 3. lim 北主 2.

Q: Evaluate the following indefinite integral Use C for any constant of integration 81 – x10 dx =

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Q: (1+x*)dy + x(1+ 4y²)dx =0

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Q: 4. sin 5. y = x ArcCC 1 + v1-x² 2+X 6. y = Arccot x + Arctan 1-2x >| ×

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Q: 1 Solve the equation: 1 x + 3 1/4

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Q: A hole is drilled through the center of a sphere x² + y² + z² = R,², leaving a ring-shape solid. If ...

A: A per your request , (b) The equation of sphere is given as , x2+y2+z2=Rs2 and Radius of drill=Rd f...

Q: 17. Find all local maxima, local minima, and saddle points for the function: f(x,y) = x² – 6xy + 8y³

A: To find the local maxima, local minima and saddle points for the function: f(x,y)=x3-6xy+8y3

Q: \k+2

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Q: Examples I Problem 1. If a + b c+d 4 6. c -d a- b] 10 2 ; ")-) find a, b, c, and d.

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Q: 4. For the function z = e cos(y) find the equation of a. The tangent plane to the given surface at p...

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Q: A minute hand on a clock is 5 inches long. Determine how far the tip of the minute hand travels betw...

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Q: Question 2 For positive integer n, let a, (-1)"n 3" (a) Determine whether the sequence {an} is conve...

A: Let <an> be a sequence such that an≠0 for all n∈ℕ and an+1an→l . If l<1 ,then limn→∞ an=0.

Q: 33. For what values of x does the graph of f(x) = x +2 sin x have a horizontal tangent? %3D

A: We need to find values for which the function have horizontal tangent.

Q: Let f(x) = x² – 3x+ 4 and g(x) = Vx – 3. Find the following - - (a) f(0) (b) f(2) (c) g(12) (d) g(4)

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Q: Write the parabolic equation in standard form and identify the vertex, focus, directrix, and directi...

A: As you have asked multiple questions so I have answered first question as per the guidelines.

Q: Solve the differential equation. dx = (x2yey^3 - 3xy2) dy

A: dx = x2yey3 - 3xy2 dy

Q: Make a hyperbolic parabloid

A: Here is the image 

Q: Evaluate the expression. 3 4 O A. -81 O B. 81 Ос. 81 1 O D. (-81)

A: We can find the answer as below in simplified form.

Q: Find the differential equation of the family of plane curves described. Draw at least three members ...

A: We have to find the differential equations of the family of curve that

Q: (b) If u = x? cos y+ye», where x= s+2t and y = st, prove that ди 2- ди = (s – 21) (x² sin y – xye" –...

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Q: Solve using variation of parameters or reduction of order (D² + 1)y = sec*x

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Q: Determine whether the series converges, and if so find its sum. If the series diverges, indicate tha...

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Q: Without solving for the solution, what would be the correct form of the solution of the DE when usin...

A: We have to find correct form of the solution and we have find complementry solution in ans 2

Q: Determine if the following series converges or diverges. If it converges find its value. n²+ 4n+3 5/...

A: Wi will use partial fraction to solve the given problem.

Q: 1. Find the determinant of the following matrices by using elementary row operations. 4 -7 9 1 6. (d...

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Q: (c) Let f(x.y) = (x²+G))), Determine the directional derivative of f at the point (1,0) in the direc...

A:  f(x,y) = (x2 + (y/2))3 we have to determine the directional derivative of f at the point (1,0) in t...

Q: Write the first five terms of the sequence: {Vn² + 7n – n}n=1 Determine whether the sequence converg...

A: The given sequence n2+7n-nn=1+∞

Q: Question 4 (a) Evaluate, with the order of integration being reversed, an equivalent integral of the...

A: Let's find. 

Q: E Homework: Homework 5.4 4 6 in terms of sums and differences of logarithms. 4 9 m'b Express log 4 6...

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Q: Determine whether the series converges, and if so find its sum. 4k+2 Σ 7k-1 k=1

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Q: ckdown RODLL ND. Find the centroid (center of mass) of the top half of the unit circle. See the pict...

A: See the details solution in below

Q: f[x'+zy2,y²2x2], then prove that [y?-zx] (a?-yz] dy [z-xy] du -o. If

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Q: Find an equation of the surface of revolution generated by revolving the plane curve about the indic...

A: Given equation: x2=4y    which has to be revolved about the y-axis.  

Q: What are the critical numbers of the function? f(t)=8(t^2/3)+t^5/3

A: We have to find critical numbers.  

Q: If u =x² cos y +ye», where x =s+2t and y= st, prove that ди 2- Əs ди 3 (s— 21) (х' siny — хуе" — е")...

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Q: Find the equation of the tangent line and equation of the normal line to the graph of 3x cos y = 1 +...

A: We have to find the equation of normal and tangent line. 

Q: Determine the Mc Laurin Series Expansion of the function and express the terms in power series formu...

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Q: 9-36 Evaluate the integral. So 36 - 9. x'V16 + x?;dx 10. dx V9 6, Vx² 1 dx 13 - dx 36 - х2 11. 12. d...

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Q: Evaluate the double integral // (3r - 7y)dA, where D is the domain bounded inside the tangle with ve...

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Q: a² +x – 6 + a |æ – 2| if x 2 - 2| 2

A: Note:- Since you have asked multiple question As per our policy, we will solve the first question fo...

Q: Find the solution to the quadratic equation. (a) a - 4x + 1 = 0 (complete the square) (b) (3x – 1)2 ...

A: We complete the squares of given quadratic equations and solve for x  When take the square root on b...

Q: Find the General Solution: y" - 3y' + 2y =e*

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Q: A coin sold for $201 in 1980 and was sold again in 1989 for $440. Assume that the growth in the valu...

A: Given: A coin sold for $201 in 1980 and was sold again in 1989 for $440. Assume that the growth in t...

Q: Evaluate the integral: /V13 – 49a*dæ

A: Integration

Q: A corner of a portrait oriented A4 sized coupon bond in millimeter is folded over so as just to reac...

A: Given: A4 size paper with dimensions 210 x 297 mm  (general dimensions) The corner is folded over so...

Q: Solve the differential equations. dy = (y²xe** – 3x²y)dx

A: Given:- dy=(y2 xex3 -3x2y)dx  To find:- General solution for given differential equation

Q: The distance, in feet, a moving object has traveled after t seconds is given by 3t/(4 + t). Find the...

A: We can find the required acceleration as below.

Q: Use the difference an+1 a, to show that the sequence | {n – 9"} - n=1 is strictly increasing or stri...

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Q: Consider the following function. s(2) = { 16 , 0 %3D (a) Find the critical numbers of f. (Enter your...

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

Q: Find the point of intersection between the line x+2/6 = y - 3 = z/3 and the plane x + 2y – 4z = 0.

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Q: Find the six trigonometric function values of the specified angle. 24

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