Evaluate the integral. 了學 ( Inx dx O- In x - +C 2x 4x2 O-4 In x - + C 4x2 0.을 Inx- +C 2x2

Q: d²x dx 5 dt2 2- 3x = -9t2 – 1 - - dt dx When t = 0, x = 1, = 0, find x when t = 2 dy %3D -

A: Please see the below picture for detailed solution. 

Q: (a) Calculate the first-order differential equation below using transformation y = xv. dy +3у %3D 2х...

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Q: 2. A particle of unit mass moves so that displacement aftert seconds is given by x = 2 cos (t - 2). ...

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Q: cOs X sin? x

A: Given:- ∫cosxsin2xdx Formula:- we use substiution method and formula ∫xndx=xn+1n+1+C

Q: Q1 (9 M)/ Use Gauss's theorem to evaluate ff. F.ds where F= 4xi - 2y'j +z°k and S is the surface bou...

A: We have to evaluate the integral ∬SF·ds where F=4xi-2y2j+z2k and S is the surface bounding the regio...

Q: 4. Summation of two variables: E(x, +y;)=E×, +£v, i-1 Example Evaluate the following given that x, =...

A: We can find the answers as below.

Q: C 1000 A В

A:  We know that law of sine is : SinA/a = SinB/b = SinC/c. Here A,B,C are angle of triangle and a,b,c ...

Q: x* + x³ + x² – x + 1 – x + 1 x(x² + 1)²

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Q: Tell whether each given function has a solution on the indicated closed interval. Prove using the IV...

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Q: The slope of curve is given as (2x + b + ) and has a value of 17 2x3 at x = 2. What is the value 16 ...

A: Topic   = Integartion

Q: b. Let g(x) = x² – 7. Determine the root(s) of g. 7,-7 Preview 7 = 7., – 7 = -7. c. Let h(x) 5x? - 3...

A: Topic = Algebra

Q: derivative

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Q: Question 1: When working with rational functions of the form f (x) = P(z) what information can you 2...

A: We can find domain of f(x)   

Q: F(x, y) = x²yi + 3y³x²j Find the integral curves for the vector field -6y + 1 C 6ху? a. ob. -6ху —1 ...

A: Apply integral form 

Q: 3. (a) Evaluate the following with the trigonometric form of Beta functions(Give your answer in term...

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Q: K石Xuts

A: ∫ Sin-1 x dx   ....(1) Using integration by parts ∫ f1(x)*f2(x) dx = f1(x)∫f2(x)dx-∫[d/dx(f1(x)*∫f2(...

Q: What is the derivative of the following function

A: Given that: 1. h(y)=y1-ey2. f(t)=1+5tln(t)

Q: 52. 0 = 6. 54. 0 = 12.9

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Q: 55-68, evaluate the sine, cosine, and tar of the angle without using a calculator. 58. 675° 2n 64. 3

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Q: 18. A bus traveling at 66 ft/sec along a straight , level road decelerates at constant rate of 22 ft...

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Q: xª + x³ + x² – x + 1 2 x(x² + 1)²

A: Here we have to find the partial fraction decomposition of the given fraction.

Q: 6. f(x) = V7x + 6; f'(3)

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Q: Find all angles ? between 0° and 180° satisfying the given equation. Round your answer to one decima...

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Q: The Law of Cosines states that e? = a + b? – 2abcos 0, where a, b, c are the sides of a triangle and...

A: Given:    c2 = a2 + b2 - 2ab cos θ

Q: The rate of change in the profit (P) with respect to the number of units sold (x) is 0.0006x² + 10. ...

A: According to the question: It is given that dPdx=0.0006x2+10. we have to find P when x=100. Now  dPd...

Q: If f. g and h are functions defined on the set of real numbers defined by: F(x)= 3x+1, g(x) = 2x -1 ...

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Q: Perform the indicated operation. If possible, reduce the answer to its lowest terms. 2 15 4 2 15 (Si...

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Q: (x² +3y² +5)dx +(6xy+ 6y+3)dy = 0 Identify the exactness of the differential equation. Calculate the...

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Q: Calculate the first-order differential equation below using transformation y = xv. dy x+3y = 2x – y ...

A: We need to solve the D.E.

Q: Function Type Differential Operator AxN + BxN-1 + .+C DN+1 AxNeax (D – a)N+1 cos(Bx) or sin(Bx) (D2 ...

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Q: 18( cos54 + isin54°) 3(cos102" + isin102" )

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Q: Given a function ƒ (x) whose graph is shown below. 3 2 h -3 12 -11 2 3 -2- -3 Determine lim f (x).

A: Graph of the function is given, we have to find the left limit at x=1

Q: Find all the local maxima, local minima, and saddle points of the given function. f(x,y) = x2 - 6xy ...

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Q: Find the inverse function of  f.​ f(x)=8x-1/3x-4 x cant equal 4/3

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Q: Find a (real) general solution. y" + 2y' + 2y = 4e¯* sec³x

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Q: Write an equation for a cost function where the fixed costs are $2300 and the variable costs are $20...

A: Given data: Fixed cost= F= $2300 Variable cost=V= $20

Q: (a)Odd degree polynomial functions have opposite________ .  (b) When we multiply two functions toge...

A: As per our guidelines we are supposed to answer only first three parts. Kindly repost others part as...

Q: Function Type Differential Operator AxN + BxN-1+..+C DN+1 AxNeax (D – a)N+1 cos(Bx) or sin(Bx) (D? +...

A: To determine the differential operator for the right side of the given differential equation.y''+4y'...

Q: LINEAR DIFFERENTIAL EQUATION WITH CONSTANT COEFFICIENTS (STEP BY STEP SOLUTION) (D4 - 1)y = e*

A: Please see the below picture for detailed solution. 

Q: C 1000 A В

A: We know that sum of angles of triangle  <A+<B+<C=180°  <A+27°+94°=180°  <A+121°=180° ...

Q: 6x³ – 1 у — 2х + 1 3x* - 4

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Q: if x < 0 if 0 < x < 1 -x² + 4x – 2 if 1 < x < 3 . Find lim f (x). if x 2 3 Given: f(x) = • %3D x-3 4...

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Q: Find or evaluate the integral using an appropriate trigonometric substitution. +3 x2 dx 4 + C

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Q: Calculate the difference quotient for f (x) = 5- x² at a = 3. (Express numbers in exact form. Use sy...

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Q: 4. (a) Prove the reduction formula: tan?n-1 (2r) _ [ tann-2 (2r) dr 4n- 2 tan" (2.r) dr (b) The redu...

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Q: dy Given the equation below, find dx - 30x³ + 8x45y + y" : - 21 dy dx Now, find the equation of the ...

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Q: Sketch the region enclosed by a + y = 6 and æ + y= 0. Decide whether to integrate with respect to a ...

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Q: Question 11 Зсos3x-1 To evaluate f scos - dx, the integrand can be transformed to 1-sin?x A.) [(3cos...

A: We put 1-sin2x=cos2x and then solve it. Follow 2nd step.

Q: Find the equation of the tangent line at (3, f (3)) when f (3) = 20 and f' (3) = 4. (Use symbolic no...

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Q: Given the differential equation y" - 3y' - 28 = 6x e2 + sin(8x) Find the Differential Operator for t...

A: This problem can be solved as follows