Given: JV5x² - 3 xdx. If we let u= 5x - 3, which of the following u-substitution formula is applicable?

Q: Use sigma notation to write the Taylor series about z =1, for the function. 3Inr; 10 = 1 Σ

A: Explanation of the answer is as follows

Q: 8

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Q: 2x2 - 1 6 y = х - 2

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

Q: Let V be the volume of the solid obtained by rotating the region above the x-axis and below the grap...

A: Given :f(x)=e-x0≤x≤2Rotating about the x-axis

Q: Describe and explain a. continuity of a function at a point. b. continuity of a function on an inter...

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Q: Find the nth Taylor polynomial for the function, centered at c. f(x) = In(x), n = 4, c = 7 (1 -7)° (...

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Q: Use the formula for the binomial series: (1+x)" = 1+ mx + + ... 21 = 1+ Ein if al < I 1 to obtain th...

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Q: 3. Use Squeeze Theorem to evaluate lim 1-0+ sin(In r) In(sin æ)"

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Q: Find the arc length of y = 7r +1 over the interval [0, 2]

A: y = 7r + 1 arc length=∫02 1+(dy/dr)2dr dy/dr = 7' arc length=∫02 1+(7)2dr arc length=∫02 50dr arc le...

Q: Evaluate the following limits using L'Hôpital's rule 1. lim x→0 e^x(cschx)

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

Q: Express the surface area of the surface obtained by rotating the graph of y = 4 sin (x) for Sx as an...

A: To express: The surface area obtained by rotating the graph of y=4sinx for π6≤x≤π3. Concept used: Th...

Q: Solve. 5x-8 2 ... Select the correct choice below and, if necessary, fill in the answer box to compl...

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Q: In general, a partial fractions integral with a repeated irreducible quadratic factor will result in...

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Q: By using chain rule Find dy/dx iff- u=-1, x=-1

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Q: Explain the relationship between power series and the Laplace transform

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Q: dw dw In each of the following, find and dr’ ds using the Chain Rule. 1. w = ry + yz +az; x = r+s+t;...

A: Given w=xy+yz+xzx=r+s+ty=rstz=r2+s2+t2

Q: Use the binomial series to find the Maclaurin series for the function. 4 f(x) = V1 + x 1 f(x) = 1 +-...

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Q: How much money should Cody invest today into a fund that earns interest at 4.75% compounded quarterl...

A: Here, the effective semi-annual interest rate =1+quarterly rate2-1 where quarterly rate =4.75%4=1.18...

Q: 12. In the polar coordinate system, as defined in Chapter VIlc, r and e are related to x and y as r ...

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Q: Solve. 3x 12 96 %3D x-4 2- 16 X+4 .... Select the correct choice below and, if necessary, fill in th...

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Q: What events in life can you compare to continuous functions?

A: A function is a continuous function if the graph of the function is not breaking at any point in its...

Q: (11) Which of the following functions f: Z x Z Z is injective (A) f(1,y) = 1/y (B) f(x,y) = x+y (C) ...

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

Q: (b) lim log1 r+2+ (x – 2)? sin(2x2 – 3x – 2),

A: solution:-limx→2+ log13x-22sin2x2-3x-2=limx→2+ -log3x-22sin2x2-3x-2=limx→2+ log3sin2x2-3x-2x-22=limx...

Q: A box with an open top is to be constructed out of a rectangular piece of cardboard with dimensions ...

A: Here, the volume of the box is given by: V=lbh Here, for the given box, l=9-2x, w=10-2x,h=x. So, V=(...

Q: sin 3x Given: -dx_what is the appropriate formula to find the integral?- cos2(3x) (4-3 sec 3x) A du ...

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Q: 5. y( 8x -9y) dx + 2x(x-3y) dy = 0 ans. x'y(2x-3y) = C #5 by another mmethod

A: According to our guideline we can only answer first question and rest can be reposted.

Q: Evaluate the limit. (Use symbolic notation and fractions where needed. Use the symbol co for infinit...

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Q: A closed right circular cylindrical tank is to have a capacity of 128??3. Find the dimensions of the...

A: Volume of cylindrical tank is 128π m3.

Q: u+1 Using u-substitution, the integral Jf(x)dx reduces to a new integral g(u) du. If g(u) = , evalua...

A: We have to find value of f(x)

Q: Use the definition of Taylor series to find the Taylor series (centered at c) for the function. f(x)...

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Q: A region is enclosed by x = y² and x = k , where k is a positive constant. The area of the region be...

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Q: 3. (2y? + 3xy -2y + 6x ) dx + x(x + 2y - 1) dy = 0 ans. x? ( y + xy-y +2x) =

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Q: Watch the introduction to partial fractions video 2 and the video on repeated linear factors e befor...

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Q: 10. Using Stoke's theorem, evaluate y dx+ xz dy+x² dz where C is the boundary of the triangle cut fr...

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Q: /atch the video on the improper integral 1/x^2 2 and the video on the nproper integral 1/x 2 before ...

A: We use the formula integration of ex dx=ex.

Q: Find the total differential dw. 5. w = x tan¬ y – 2ªyz

A: The objective is to find total derivative dw.

Q: Find if y = xsinx – cosx d²y COSX dy Find using implicit differentiation а. уз + у? — 5у — х? %3D — ...

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Q: et Js (0, 1.2,3,4) and define a function g: Js x Js → Jg × Js as follows: For all (a. b) E Js X Js. ...

A: Onto function

Q: ladder 10 ft long rests against a vertical wall, If the bottom of the ladder slides away from the wa...

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Q: Check which one of the following functions is a solution to the differential equation y" -y= sin x. ...

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Q: A 14 foot ladder is leaning against a wall. If the top slips down the wall at a rate of 4 ft/s, how ...

A: A 14 foot ladder is leaning against a wall. If the top slips down the wall at a rate of 4 ft/s, how ...

Q: Use the given integral table to find and evaluate the given integral. Given: ∫ 1/√6x - x2 dx

A: Given ∫16x-x2dx To evaluate the integral:

Q: Falco Inc. financed the purchase of a machine with a loan at 2.03% compounded semi- annually. This l...

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Q: Find the dimensions of a rectangle with perimeter 1000 meters so that the area of the rectangle is a...

A: topic- application of derivatives

Q: Determine whether the series converges, and if so find exactly its sum. Otherwise type none in the b...

A: ∑k=0∞78k+2

Q: Find the derivative of f(x)=8x - 5x+2 using first principles (i.e., use the definition of the deriva...

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Q: Determine the arc length parameterization of the circle x^2+y^2 =a^2 with orientation counterclockwi...

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Q: Let (2) = /2*+1, 4-x, Without graphing, is f(x) continuous at x 2? Clearly justify your answer. x+1,...

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Q: Determine whether the alternating series converges. 51n k (-1 k k=3 O The series diverges. O The ser...

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Q: A contract requires lease payments of $800 at the beginning of every month for 4 years. a. What is t...

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