Use integration by parts to evaluate the integral: 7x dx = f9x²³e¹²d

Q: Consider the line y = ax, where a is a positive constant. What is the shortest distance between the…

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Q: 1 The vector field F = is conservative. Find a potential function for F compute SF dr, where C is…

A: To find the given line integral.

Q: 2. Find the values of r for which the differential equation has a solution of the given form. a.…

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Q: Given f(x) = (x - a)² where a is constant. Where does the absolute maximum value of f occur on the…

A: Given,            fx=x-a2 where a is constant.To find : Where does the absolute maximum value of f…

Q: Without using a calculator, compute the sine and cosine of 120 by using the reference digte (Type…

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Q: 5 Σ(-1)", 4" n=1 20130 O Ο 5 04 0 -1 Ο 20 3

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Q: P 1/^ (1) J 8.

A: Given query is to find the integral.

Q: 56. L²₁ dx 2 x² 3 2

A: ∫xndx=xn+1n+1+clet  I=∫-124x3dx

Q: 2. Find the sum of the series. ∞ 71=0) 312-4¹ 5n|1

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Q: 1. Find the definite integral using the Fundamental Theorem. Show in detail how the antiderivative…

A: Since you have asked multiple questions, we will solve the first question for you. If you want any…

Q: 6. Sketch the graphs of the functions, f(x) = 2* and g(x) = x - 1 on the axes below. Then, on the…

A: we need to graph the functions.

Q: L₂ (3x + 4) dx

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Q: Sketch the graph of f and use your sketch to find the absolute and local maximum and minimum values…

A: To sketch the graph of f and by using your sketch to find the absolute and local maximum and minimum…

Q: What is the minimum possible perimeter for a rectangle whose area is 100 square inches?

A: Given query is to find the minimum possible perimeter.

Q: 5. Using geometric series, 1 1-z =1+x+x² +· Στ TL=0 find a power series expansion for the function,…

A: To find the power series expansion of given function

Q: Find the point on the plane x - 2y + 3z = 9 that is closest to the point (0, 2, 1). 5 3 23 8'4'8 )…

A: The equation of the plane  x-2y+3z=9

Q: Solve the FIRST ORDER LINEAR D.E Linear in y y' = x³ - 2xy → when x = 1, y = 1

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Q: Write 1 =x+5 9 as a piecewise-defined function. 1. f(x): = 2. f(x) = f(x) = - 1 x+5, x ≥ −45 9 1…

A: for f(x)=xf(x)=x,  x≥0-x,  x<0

Q: Please write in a better format. I do not understand how the problems is developed when letters and…

A: To determine the second derivative of the following parametrically defined curve.xt=2 sin3tyt=-cos3t…

Q: ㅠ mine the equation of the tangent line at t = to the curve defined 3 metrically by the equations…

A: Topic: application of derivatives

Q: Which of these vector fields are irrotational? Identify all of those that satisfy this property. A B…

A: The given vector fields, A) u=-x, y, 0B) u=-y, x, 0C) u=-x, z, 0D) u=x, y, z We have to find the…

Q: Given f(x) = ax³ + bx² + 9x + c. Find a so that (2,3) is a point of inflection of the graph of f and…

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Q: Evaluate the definite integral. 2 8xex2 dx   0

A: Given query is to find the integral

Q: 27. [" (Se* + 3 sin x) dx

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Q: If f'(x) = cosx-9x²- 1 Xx

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Q: Evaluate the following integrals analytically: Cπ/2 #1 #2 #3 (8 + 4 cos x) dx 3 [² (1 - e²^x) dx [²₂…

A: The given integrals, 1. ∫0π28+4 cosxdx 2. ∫031-e-xdx 3. ∫-241-x-4x3+2x5dx We have to solve these…

Q: 4. FIND THE 2ND DERIVATIVE f(x)= (3x²-2)bog (3x²-2); x Solution: x=1

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Q: A dam having a width of 500 m is holding back a column of water of height H meters. The total force…

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Q: Consider the following.   36 7   2x + 1 dx   0  Let  u = 2x + 1.  Find du. du =

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Q: (x - 1)" (n + 1)2n Determine the values of x for which the power series Σ(-1)". n=0 converges.…

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Q: How much more interest will be earned if $5000 is invested for 6 years at 7% compounded…

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Q: Expand, that is, perform the indicated operations on the differential operator D. a) (2D + 3)(D −…

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Q: 103.3 5 [ ₁ (+² -5 (x² + 2) dx X

A: ∫xndx=xn+1n+1+clet I=∫-55(x2+2)dx

Q: Given f(x) = ax³ + bx. Find a so that f has a relative extremum value (d.) 17/06 at (2,-1). (a.)…

A: Given:      fx=ax3+bx Relative extremum value at 2,-1 To be a relative extremum, f'x=0 For the value…

Q: Solve the FIRST ORDER LINEAR D.E. Linear in y y' = x³ - 2xy →→ when x = 1, y = 1

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Q: Problem 7. series converges or diverges and mention the test you are using. Show all work. 00 (2) Σ…

A: To solve this problem we can use p-test , comparison test and root test

Q: Consider the following initial value problem, defined for t > 0: y² – 2y = f* (t- a. Find the…

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Q: 10. The area between two curves is expressed as: A = [f(x)-g(x)]dx If a horizontal element of area…

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Q: Evaluate the integral 28 fx³ (26 – 9) ²8 d. - = – 9. by making the substitution u= 26 + C

A: To solve the following problem of Integration

Q: Evaluate the definite integral. 3   0 ex 5 + ex dx

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Q: Using Integral test, determine convergence or divergence for Σn (Inn)³3 * n=3

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Q: (b) (i) If y=-e 1 show that dy k = dx 22 e NIX

A: "Since you have asked multiple question, we will solve the first question for you. If you want any…

Q: Evaluate the indefinite integral. Use C for the constant of integration. S sin (+) √ 1 + cos(+) d+

A: Find the indefinite integral

Q: If f(x, y) = 4x² - 7y², then the total differential of fat x = 1 and y=-2 is; O df = 28 dx + 8 dy df…

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Q: 1. Write as a piecewise function f(x) = |x +4| X- - 5*

A: put x+4=0x=-4when x≥-4 , f(x)=x+4when x<-4,  f(x)=-(x+4)=-x-4

Q: Consider the function in the graph to the right. The function has a relative maximum of 3 o at x = 0…

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Q: 5. Evaluate the integral using the following: . Formulas: a. [²x²³ dx = 4/7/ [²³x³dx x³ dx b. L'a…

A: To evaluate the given integrals.

Q: Determine the integral that can be used to find the arc length of the curve defined by the…

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Q: If fºrex f(x) dx = 12, what is the value of A) 12 B) 0 C) 6 √ [ ƒ(6-x) dx? D) -6

A: If  ∫06fx dx=12, then to determine the value of ∫06f6-x dx.

Q: Evaluate the definite integral. 25   0 9e   x   x dx

A: