g (x) = -2x3 Vx²+1

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

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Q: dy = (y2xe^ - 3x²y)dx

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Q: Problem 5.1 List all the elements of Un for n E {2,3, 4, ..., 12}.

A: Un is a group in which all elements are relatively prime to n and less than n

Q: Given the function g(t) = (t-4)(t+3)(t-1) What is It’s g - intercept is: What is It’s t- intercept i...

A: The objective is to find g - intercept and it’s t- intercept .

Q: Differentiate y %3 (x? + 7х — 1)(5х + 2) а. 20х3 + 6x2 +70х + 9 b. 12x3 — 4x2+ 70х + 9 с. 10х3 + 6x2...

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Q: 1. Consider the following shaded areas: 5 4.5 - 4 - 3.5 - y 25 Here, the red curve is y = f(x) and t...

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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: 6. A water tank is shaped like a cone with the apex point at the bottom, where the cone has radius 5...

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Q: For real number p, let f and g be defined by f(x) = e- and g(x) = 1/xP, respectively, on [1, 0). f(x...

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Q: (x - 2y +4) dx + (2x-y+ 2) dy =0

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Q: Use any method to determine whether the series converge. (a) E 9k The series

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

Q: xy' + (1 + x)y = e* sin 2x %3D

A: xdydx+1+xy=e-xsin2x

Q: 1. A model for the position x (t) of an Olympic jump skier says that the acceleration a(t) = x" is p...

A: As per as our guidelines i am supposed to answer only three parts of this question Please repost the...

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: y + = x2+y2 dx xdy when x=J3', y=1

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Q: 2 Let R be the region of the 1st quadrant surrounded by a curve. X : + 2 straight straight line 4 - ...

A: Follow the procedure given below.

Q: ITC A= - radians The Ieast positive angle that is coterminal with A is radians. (Type an exact answe...

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Q: 5. (4x'y — 15х2 — у)dx +(x* +3у?- х)dy-0

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Q: dy/dx = sec 2xsec3y

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Q: There are ​$320 available to fence in a rectangular garden. The fencing for the side of the garden f...

A: We need to find x and y.

Q: and stra ight and x : 8 Let R be an area enclosed by a curve. : 1 Using the cylindrical shell method...

A: Given problem:- Let R be an area enclosed by a curve. X =4√y and straight line y=1and x = 8 Using th...

Q: 2. Consider lim xa q(x) A student says that this answer means the limit is 1. Is the stude correct? ...

A: Since we are given with the multiple number if question and our guideline is solve first question ki...

Q: quation. Do not simplify.)

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Q: Solve the differential equations. (y Jri i y²) dx xdy When x=V3, y = 1

A: y-x2+y2dx-xdy=0

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

A: Given

Q: an² y dx = sec²x dy

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Q: Please do numbers 3 and 5

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Q: Eliminote the orbitrary constants x = k +ct, y= c*t² Find the differential equation of the plane cur...

A: Order of differential equation (D.E) = the number of arbitrary constants in the given relation.The D...

Q: Explain why the integral e'dx is convergent.

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Q: (b) Find an operator A that annihlates the following functions. i. In(x) ii. to , α ε R iii. sin(3 I...

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Q: dx =(x²yeº- 3xy²) dy |

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Q: For the following two vectors, (a) calculate their dot product, and (b) find the angle 0 between the...

A: We have to calculate dot products and find angle

Q: Set up the definite integral that gives the area of the region. Y1 = x2 + 2x + 4 Y2 = 2x + 8 dx -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: 2. A hemisphere of radus 12 nches and base up is full of water that runs out through an orifice of a...

A: Dimensions of a hemisphere tank are: Radius R=12 inches or 0.3048 mHeight of tank H1=Radius of tank ...

Q: A recipe calls for 4 of a cup of flour to make one batch of doughnuts. If Cecilia wants to make 9 ba...

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Q: (1+x*)dy + x(1+ 4y²)dx =0

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Q: how to solve cos(arcsin[3/5])

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

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Q: the plane according to the equations x = t² + 2t and y = 2t³ – 6t. Find dy/dx c. 3 d. 4

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Q: Find the slope of the curve x? – 3xy + y² – 4x + 2y + 1 = 0 at the point (1, -1). с. 1/3 d. 1/5 а. 1...

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Q: Evaluate the integral : S 8г2 +10х—6 (х—1) (х+1)2 dx = |

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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: Show that the limit xłycosy lim (x.y)→(0,0) 2x4 +y² does not exist.

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Q: Sx+5 if x m C. 8 Find the value of m such that g(x) = is continuous at x = m. A. 2 B. 4 D. -1

A: Let's find. 

Q: (-1)"n For positive integer n, let an = 3n (a) Determine whether the sequence {an} is convergent. 00...

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Q: Find the general term of the sequence, starting with n = 1. Determine whether the sequence converges...

A: The given sequence is: 19, 193, 1932, 1933, ....

Q: Sketch the graph and determine the domain and range. 1. y = 2- x,for x 2-4 2. y=x-6x +5. for 1 sx< 5...

A: As per Bartleby guidelines rule I am answering only top 3 questions. Domain : The domain of a functi...

Q: 11T A point has polar coordinates ( 8, 6. Convert to rectangular coordinates. (r, y) = Enter your an...

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Q: Find the curvature of y = cos x at the point (,). Then find the equation of the osculating circle at...

A: To find: The curvature y=cosx at the point π4,22 also find the equation of the oscillating circle at...