Using the € - d definition of limit, prove that 2x lim x 2 x + 6 1 NI

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A: Given that a particle moving along a path  with  subjected to force

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A: In the Norman window, the length and breadth of the rectangle is . Also the diameter of the…

Q: Find y'' if y=-8 cos x. OA. y'=8 sin x OB. y'= -8 cos x OC. y'= 8 cos x OD. y'= -8 sin x

A: Explaination of answer is as follows

Q: 5. Use a triple integral to find the volume of the solid in the first octant bounded by the plane 2x…

A: Solid in the first octant bounded by the plane 2x+3y+6z=12 and the coordinate…

Q: Let F (8yz)i + (9xz)j + (9xy)k. Compute the following: = A. div F = B. curl F - C. div curl F= i+j+…

A: F=(8yz) i+(9xz) j+(9xy) k

Q: Hi b and c are incorect

A: From the given table

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Q: 256x The volume of a sphere is increasing at a rate of 8 cm³/sec. Find the rate of change of its…

A: The rate at which the volume of a sphere is changing, To determine: The rate of change of the…

Q: SOLVE THE FOLLOWING PROBLEM AND SHOW YOUR COMPLETE SOLUTIONS. EXPLAIN YOUR WORK FOR BETTER…

A: The given integral is

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Q: For Evaluate the following expression. Select the correct answer below: f(x) 4-x-x² ifxsl 2x-1 ifx>1…

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Q: Let u = (1, -7). Find the component form and magnitude (length) of the vector 3u. The component form…

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Q: Match the graph of the function on the left with the derivative on the r 1. a. 2. 3. 4. -10 10 -10…

A: Note:-Since you asked multiple sub parts questions, according to our policy we can solve only first…

Q: 6. Suppose f f(x) dx = -5, and fg g(x) dx = 1. Evaluate the following integrals using the properties…

A: To find values of given definite integrals.

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A: Firstly find inflection point (f"(x)=0).Concave upward: f"(x)>0.Concave downward: f"(x)<0.

Q: Find the area under the given curve over the indicated interval. y = 4x; x =1 to x = 3

A: y=4x, x=1 to x=3

Q: (a) Eliminate the parameter to find a Cartesian equation of the curve.

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Q: Use l'Hôpital's rule to find the limit. Use -∞o or ∞o when appropriate. 3x²+5 lim x→∞04x³ +2 Select…

A: The objective of this question is to find the limit of the expression (3x²+5)/(4x³ +2) as x…

Q: (i) Find the derivative of the function. esin x COS X In(1+2v) dv.

A: To find the derivative of the following function.

Q: 6. Let So f(x) dx = 12, 5 Calculate the following integrals. (a) [°*3f(x)dx = (b) *2f(x) – g(x)dx =…

A: Let To calculate the following: (c) If  is an odd  function, then to find .Note:  Since, the student…

Q: Of the following, which are solutions to the differential equation y" - 5y +6y=0 ? 1.y = e²t II. y =…

A: The differential equation is given byThe auxiliary equation corresponds to the differential equation…

Q: Given that ß = 101°, y = 24°, c = 15. Which of the following equations solves for a? a) a = (15 sin…

A: Given that the triangle we have to find choose the correct option

Q: Find a parametric equation for the line through the point (1,3,-3) and perpendicular to the plane 3x…

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Q: Find the area under the given curve over the indicated interval. y = 6x² + x +4e4 ; x = 0 to x = 7

A: The given curve .The aim is to find the area under the curve in the interval .

Q: Given the sequence an n>1 = n²-1 n+3 ' (a) List the first 5 terms of this sequence. Give exact…

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Q: Compute the curl of the vector field F = -2z7+5yj - 8x k. curl =

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Q: To find an antiderivative of f(x) = arctan(3x) you used integration by parts, and obtained…

A: The integration by part formula is:                             ..(1)

Q: Find the gradient field of the function, f(x,y,z) = (3x² + 2y² + z²) −1/².

A: According to Bartleby Guidelines, we can solve only first question from multiple question, please…

Q: Let u = (5,-4) and v= (-4,7). Find the (a) component form and (b) magnitude (length) of the vector.…

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Q: Region R is bounded by the graphs of y=e2x + 1, y = 0, x = 0, andx = 2

A: Region R is bounded by the graphs of y=e2x+1,y=0,x=0, and x=2

Q: The graph of a function f(x) is given below. Use the midpoint Riemann sum with 4 sub-intervals to…

A: A graph of the function is given.The aim is to find the midpoint Riemann sum with  subdivisions.

Q: Let f(x) = x³, and compute the Riemann sum of f over the interval [6, 7], choosing the…

A: Since you have asked multiple sub parts in a single request so we will be answering only first three…

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Q: Evaluate the following definite integral: [²22 (2² 1 2x (x² + 1)² dx Enter your answer as an exact…

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Q: A retail business owner wants to build two adjacent retail stores on a rectangular plot of land. The…

A: The figure

Q: Let f(x): = 10 - 2x. (a) Sketch the region R under the graph of f on the interval [0, 5]. y 10 8 6…

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Q: Find the area under the given curve over the indicated interval. X5 y = 6x + 2x+5e; x = 1 to x = 3

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Q: 5 (x-2) n²+1 n=1 Find the radius of Convergence R₁ of the series. Find the interval of convergence,…

A: The given series is summation of(x-2)n/(n2+1), n from 1 to infinity.

Q: 9. Suppose 0 < a <b, and Find the value of få f(x²)dx. A. 4 B. 2 C. 1 D. -5 [F(x²)dx=6₁ ["f(x²)dx =…

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Q: Consider the following function. f(x) = -5x Complete the table.

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Q: Estimate the area under the graph of f(x) = 1+x² from x = -1 to = 2 using six rectangles and right…

A: Given,from x=-1 and x=2

Q: Use the Divergence Theorem to evaluate [/F. F. N dS and find the outward flux of F through the…

A: ∫S∫F⋅NdSF(x,y,z)=xi+yj+zkS:x2+y2+z2=25Using the Divergence Theorem∬SF⋅NdS=∭EdivFdV…

Q: Express in terms of logarithms without exponents. log(x³y4z)

A: Let,C=

Q: Problem #8: Use Divergence theorem to find the outward flux of = (3x², e¹², cos³ (1² + x)) of the…

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Q: In 1619, the German astronomer Johannes Kepler showed that the square of the period of a planet (how…

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Q: f(x) = x² Which of the following is the linear approximation of f(x) at the point a=16? O O O 3…

A: f(x)=x3/8, a=16

Q: (b) log321 +2/og33 Answer: log3 189 ! No, that's only partially correct

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