Evaluate the following indefinite integral: 2(1 + e*) dx (x + e*)3

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Q: Are the Following Vectors Linearly Dependent or Independent? 1) (3,4), (4,3) Ans. Independent

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Q: Evaluate the integral 1

A: We can solve this as follows:

Q: (y®+ 4y³-Ay) dy y2+10 6. ,3.

A: LetI=∫y5+4y3-4yy2+10dyI=∫y5y2+10+4y3y2+10+-4yy2+10dyI=∫y5y2+10dy+∫4y3y2+10dy-∫4yy2+10dyTake constant…

Q: 10) Find the linear approximation to g(y) = Cos(y+1) at y = 0. Use the linear approximation to…

A: Here, the given function is: g(y)=cos(y+1) To find the linear approximation of g(y) at y=y0=0 using…

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A: Solving the problem by finding the derivative of the function.

Q: tan de sece + 4 cose COs

A: The integration of the integral is  tanx/(secx+4cosx).

Q: Locate the points of inflection of the curve 4 ƒ (x) = x²e* -2+ V3 2+ V3 Option 1 Option 2 -2+ v2…

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Q: 5. Use the shell method to find the volume of an ellipsoid formed when that part of the ellipse x2 +…

A: Given

Q: determine the following log1o 10? b. log e?. c. log1o 800 с.

A: Since you have posted multiple questions i can do first three question as per our company guidelines…

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Q: Consider the R 2 − R function defined by f(x, y) = 3x + 2y. Prove from first principles that lim…

A: Given function F(x,y)=3x+2y Take path  Y=-x  X→1 then y→-1 Then function F(x)= 3x-2x=x

Q: Find all values of x for which the series converges. (Enter your answer using interval notation.)…

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Q: Determine the center of mass for the region bounded by the following y=x^3 and y=√x.

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Q: dy – e3x+2y . Find the general solution of dx

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Q: xydy – (y 3x2) dx = 0 –

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Q: II. Evaluate each of the following limits. 1-V3-x 4) lim x→2 4-x2 5) lim x→∞ 3 Sin ) 2 6) lim(4x +…

A: We have to evaluate the given limit.

Q: dy (y casxy +)dx+ =e (xcosty +2y=3) dy

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Q: 1 4. Find the maximum value of f (x) = In(x- Inx) on the interval-<x<e. e

A: Given problem:- Find the maximum value of ƒ (x) = ln(x−lnx) on the interval 1/e≤x≤e

Q: 3. Jy

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Q: 4. J 5 5. S 12 7 in 3x dx 6. S (10 x - 40) dx x 2 - 8 x + 15 8. S

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Q: ACTIVITY 2.Solve the given below. Show your complete and exact solution. 5. Given the function f(x)…

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Q: equation of the tangent to the curve y = 1+ Int and x = t+ Int when t = 2

A: Topic:- application of derivatives

Q: fle 30 4) de 3e +1

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Q: xp x[1+ (In x)²] 5.

A: The given integral is: I=∫dxx1+lnx2   ...(1)   We know that; ∫11+x2dx=tan-1x+C

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Q: Learning Task 5: Analyze the given condition and calculate the sum using the properties of sigma…

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Q: What is the difference between "countably infinite" and "uncountably infinite"?

A: We have to write the difference

Q: a. Find the first four nonzero terms of the Taylor series for the given function centered at a. b.…

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Q: Water is pouring into a swimming pool. After t hours, there are 2t – vt gallons in the pool. At what…

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Q: sec(2) tan(z) – 1 dz 1 dz

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Q: 3. (a) y(8) when y=cos 2x 2 (b) y(9) when y=3 cos t 3

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Q: 1. Find dy for each of the following: dx d) y = e +x° +e° e) y = x° Inx 1) In(x + y) = e*-

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Q: A graph of f(1) is shown above. Using the geometry of the graph, evaluate the definite integrals. a)…

A: Solve using the area under the curve between given limits

Q: end of 35 years and 9 months, if the interest raté is 6% compounded quarterly. 4. Accumulate P 1,100…

A: Given problem:- Accumulate P 1,100 at 8% compounded monthly for 25 years and 5 months.

Q: 2X + 2 ) dx 3. 2X 6 + 2e

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Q: The area bounded by the line y = x, the x - axis, the ordinates x =1, x = 2 is 3/2 O 5/2 O 1/2 7/2

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Q: 1. How fast is the volume of a cube changing when the edge is 15 cm if the edge is changing at the…

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

A: See is solution

Q: 3. Solve the equation: (Dª – 1) y = 0

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Q: (b) y when y=3 cos t

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Q: 1. How to solve the values of x to find the critical values of the graph of a polynomial function?…

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Q: Given a Fibonacci sequence, evaluate the sum of 1/ (an 1 x an+1) from 2 to infinity. А. О В. -1/2 C.…

A: We have to find the sum of series.

Q: Find the distance from the point (0, -1, -2) to the plane - 4y – 4z = 5.

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Q: (3x-2) dx x²+ 2x + 15

A: the given problem is solved below in detail.

Q: lim X-3 x +3 -3

A: As per guidelines we can answer only one question at a time, so if you need more answer kindly…

Q: 2x° dx x2-4

A: ∫2x3x2-4dxSubstitute u=x2-4→dudx=2x→dx=12xdu=12∫u+4udu=4∫1udu+∫1du

Q: 4. csc 2x lx

A: The integration of the integral is csc3(2x).

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Q: Find the following quantity if v 2i – 3j + 4k and w = - 2i+ 4j- 4k. 4v + 3w ... 4v + 3w = (…

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