If the 6th term of an arithmetic sequence is 63 and the 14th term is 135, write the formula for the arithmetic sequence in standard form: please show work/

Q: Find the derivative of the function at Po in the direction of A. f(x.y,z) = xy + yz + zx,…

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Q: Using Laplace transform to solve the IVP: y" – 9y = e *, y(0) = 0, /(0) = 0 %3D we find the solution…

A: The given IVP is y''-9y =e-3t,   y(0) =0, y'(0) =0 To solve the problem we must know the following…

Q: Rationalize the denominator. Vx - 9 6/x

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Q: C Fnd the firet order parho derivohve of 4.5 f(x,4,2)= e* +y2 1.

A: We have to find the partial derivatives.   According to our guidelines we can solve only one…

Q: 29 – 44 dy 2+ 49 с.

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Q: (vi) S 16-x 2+15 dx. u=

A: The objective of the question is evaluate the indefinite integral.

Q: 2у — 4 dy 2 + 49 с.

A: To evaluate: I=∫2y-4y2y+2dy=-∫4y-2y2y+2dy=-∫22y-2y2y+2dy=-∫2y-12y+22ydy=-1ln 2∫2y-12y+22yln 2dy

Q: a spherical balloon is filled with gas at a rate of 300 mm3/sec. Find the rate at which the surface…

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Q: sin 3x cos“ 3xdx

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Q: A. Assimilation (Time Frame: Since we already presented S sin x dx and ſcos x dx, we can now do the…

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Q: Find a formula for the nth term of the sequence in terms of n. 3 32 33 34 1 10' 15' 20' 25' 30

A: We have to find the nth term of the sequence.

Q: Evaluate the following integrals. (csc 0)(1+ sin? 0 + sin 0 cot? 0) de a.

A: This question is based on indefinite integral.

Q: Sketch the region bounded by the given lines and curves. Then express the region's area as an…

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Q: B- Find the length of the curve given by the position vector r=, =r'i+(1+(1/3)x')j+(1-(1/3)')k for

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Q: Vhich of the following are possible f '(x) for a function f(x) that is decreasing for every x > 5?…

A: We are asked to find which is decreasing

Q: The area under the graph of f(x) = 3x2 between x = 2 and x = k is 208, where k> 2. Find the value of…

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Q: A 15-foot ladder is leaning against a wall. If we pull the ladder away from the wall at a rate of…

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Q: (b) perimeter of AABC ВС perimeter of ADEF EF 2 So perimeter of ADEF = 15cm 7.5 perimeter of ADEF 4

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Q: Using the Laplace transform to solve the IVP: y" - 4y = 4, y(0) = 0, y'(0) = 0 we get 4 Y(s) = s(s?…

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Q: 2 | (csc 0)(1 + sin? 0 + sin 0 cot? 0) do

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Q: 4. Let F = (3y cos(3z) + 4z)i+ (3+ sin(3z))j. Use the Fundamental Theorem of Line Integrals to find…

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Q: The slope of a tangent line at (1, 4) is 2. What is the equation of the line? Select the correct…

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Q: ind the values of a and b so that the function = x + ax + b has a local maximum at the (-16,- 12).

A: We will find the value of a and b.

Q: The graphs of the first and second derivatives of a function y the figure, f is decreasing concave…

A: Given query is to find statement is true or false.

Q: 1 an 1 Use the transformation u = 2x+ y, v=x+ 3y to evaluate the given integral for the region R…

A: Given

Q: 3. If a = 2 i-3 j+5k and b = -3 i+6k, determine a simplified vector for each of the following in the…

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Q: Use any method to determine if the series converges or diverges. Give reasons for your answer. - 14n…

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Q: 1. Find the inverse of the matrix 6 12 3 3 A. 10 10 C. 30 30 3. 10 7. 3. 30 10 30 152/5 D.…

A: Solution is done in step 2

Q: 4 4 Use the transformation u= 4x + 3y, v=x+3y to evaluate the given integral for the region R…

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Q: 3dx xV4-x?

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Q: Evaluate: 1) [x.e*c

A: We will solve the integration using integration by parts.

Q: a) Use the Second Derivative Test to find the local extreme values of the function f(x)=(x^3+27)^4.

A: We have to use the Second Derivative Test to find the local extreme values of the function.

Q: For what values of x is Ax) concave down if f "(x) = 3x' – 14x² + &r?

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Q: Create a function where the domain is not a set of numbers and the range would be the set of whole…

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Q: Cx)= Ex> is add even?

A: We need to determine if the function is even or odd.

Q: dz dz Draw a dependency diagram and write a chain rule formula for and given the functions below. ds…

A: 1. D  2. D

Q: 3) (0,1,0), (2,1,0), (3,4,7) Ans. Indepena

A: Given

Q: Vx-a?

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Q: x°V16r6 – 24x³ + 9 dx .5

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Q: x² – 4 For the function f(x) =- x' +3x – 4 a) Find the equation of the vertical asymptote(s) b)…

A: Solution is here

Q: The graph of a function f is given below. According to the graph, the derivative of the function…

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Q: 3. y = e-x and the x axis is revolved about the y – axis. (Answer: t C. u. )

A: Let's find.

Q: Solve the following initial-value problem. f′(x)=2 3√x+3x^2, f(0)=6

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Q: Find the total differential du. 1. w = y tan a? – 2xy

A: To find the total derivative

Q: In cos x (1) lim x→0 tan x2

A: Let's find.

Q: Find the absolute maximum and absolute minimum of the function f(x)=2x^5/2 /5−2x^3/2 /3−1 over the…

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Q: Find an equation of the sphere whose endpoints of a diameter are (-2,0, 5) and (-1,2, 3).

A: To find the length of the diameter use the distance equation Therefore, D=-2-(-1)2+0-22+5-32…

Q: Use any method to determine if the series converges or diverges. Give reasons for your answer. (n +…

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Q: Consider the function f(x) =2x + 6x? on the interval [1, 3]. Let K ER be such that K = max |f"(x)|.…

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Q: In what instance does the Chain Rule of differentiation applicable? Explain briefly.

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