2. . For what values of m does the function y = Aet satisfy the following equation? d'y dy + бу = 0 dx² dx

Q: y = 3Arcsin (2x³) -- Arccos(2x³)

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Q: 3. Lim In(x+1)3 x →∞0 6x

A: We can evaluate the limit as below.

Q: Using Trapezoidal method √²³x² dx for n = 4 is equal to

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Q: Solid S is bounded by the given surfaces. (1) Sketch S and label it with its boundaries. (2) Give…

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Q: A stone dropped in a pond sends out a circular ripple whose radius increases at a constant rate of 2…

A: Given ,  A stone dropped in a pond sends out a circular ripple whose radius increases at a constant…

Q: Find the equation for the plane through Po(-6,3,7) perpendicular to the following line. x = −6+t,…

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Q: S. S. (x + 2y)dydx = 10, Jo a

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Q: 2. Use the disk method to determine the volume of the solid obtained by the revolving the region…

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Q: 1. The Maximum point of y=

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Q: 3 Find the approximate value of fe-x² d x, by using the Simpson's rule with n = 8. Click here to…

A: As we know from the Simpson's rule: ∫abfxdx=∆x3fx0+4x1+2fx2+4fx3+2fx4+...+4fxn-3+2fxn-2+4fxn-1+fxn…

Q: Expand the quotient by partial fractions. x²+3 x² - 13x+42 ²+3 x²-13x+42 (Simplify your answer.)

A: Given :x2+3x2-13x+42

Q: In (x-2) lim x2+ In (x² −4)

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Q: Find Laplace -3+ 2 [t². 2³+. Sincat) e -

A: See the details solution in below

Q: Lim (sinx)* -0+

A: Given query is to find the limit of the expression.

Q: 1. Newton's Law of Cooling: At 9:00PM., a thermometer reading 70°F is taken outdoors where the…

A: Note: Unit of temperature °FTs1=Outdoor temp or surorunding temp 1          = 15°FTo=Thermometer…

Q: Find the measures of the angles of the triangle whose vertices are A=(-2,0), B=(3,3), and C=(1,-1).…

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Q: an airplane is moving horizontally at 150 mph over an observer at a height of 4000ft.how fast is the…

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Q: Numerical Integration: r2 1 S² = = X 0 1. dx

A: Please find the solution:-

Q: Lim (sinx)* x-0+

A: All the necessary steps have been provided in the solution along with explanations. Follow the steps…

Q: Show all the necessary figures and solutions to each of the following problems. 1+x² 1. Find the…

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Q: Question 2 Given a differential equation as d²y-5x dy +9y=0. dx² dx By using substitution of x = e'…

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Q: 7) Find f(x) if f(x) = (103x + 2)2. a) 6 In 10 10x + 4 b) 6. 106x 105x + 3 c) (6x + ○ 4) 4) 106x d)…

A: Topic:- application of derivatives

Q: 1. For the cross product between vectors a=[h, -1, 8] and b=[k, 5, 7] to be axb= [-47, -5, 17], what…

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Q: 1. Consider the function f : R² → R such that f(x, y) = 2xy² + x² − 2xy = y + 1. (a) Write down the…

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Q: (3x² + 5x-2) dx

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Q: 12. Find the first and second derivatives of f (x) at x = 1.2 and x=2.0 from the following table 1.2…

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Q: 6. lim x->0 (1+x)¹/5 (1+x)¹/3 - (1-x)¹/5 - (1-x)¹/3 (Ans:/)

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Q: Consider the function f(x) = x^4 − 5x^3 + 9x^2 Find d)  The open intervals on which f is concave…

A: Given problem:- Consider the function f(x) = x^4 − 5x^3 + 9x^2 Find   d)  The open intervals on…

Q: f(x) = 27x² + 3x5 - 24x³ + √2x f(x) = + √2x 3 x x5

A: Find the general anti-derivative F(x) + C for the following problem:

Q: dx x² - 4x + 13 X

A: Given  ∫dxx2-4x+13To find integral:

Q: In the exponential form f(x) = a. bx, the base b can be equal to 1. (A) True (B) False

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Q: 3√3 dx X²³√x² +9

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Q: d²y dy Consider the differential equation +9y = 9x + 3. dx² dx (a) Find the general solution. (b)…

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Q: Evaluate the iterated integral by converting to polar coordinates. 2x - x² [²√²-2² 9√ x² + y² dy dx…

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Q: |y²Z² YZ Y+ZI z²x² ZX Z + x = 0 x²y2 XY X+YI

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Q: Given f(x)=4x+1 and g(x)= x²+x-3: Use the washer method to determine the volume of solid obtained by…

A: Let's find volume of solid by using washer method when given two curves rotated about x axis.

Q: A colony of the bacteria B. dendroides is growing in a petri di area A (in square centimeters) can…

A: Here we have A colony of the bacteria B. dendroides is growing in a petri dish. The colony's area A…

Q: 2. Simple Chemical Conversion Radium decomposed at a rate proportional to the quality of radium…

A: This is a problem related to decay law. Based on the general formula and concept we will answer the…

Q: II. Solve the following problems. Enclose final answer. 3 3. The Critical Point of y = xe-*

A: The critical points can be obtained by letting its first derivative equal to zero.…

Q: A lumbering battle tank's treads applied wildly varying forces in order to propel it to move…

A: We know that,  Work = force * displacement    W = F * x  = 10x(1-e-0.03x2+0.2cosx)

Q: The triple integral ¹²-x² √4x²-y x dzdydx is equal to 0.33 0.08 None of them O

A: Let's evaluate given triple integral.

Q: 3. The Critical Point of y = xe-*

A:

Q: 7. Which of the following is the differential equation satisfied by the given by the particular…

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Q: If find the value of a. 3 S₁ S² (x + 2y) dydx = 10, 0 a

A: Given: ∫01∫a3(x+2y)dydx

Q: (√t-9) dt

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Q: (D5+ D4-7D³ - 11D²8D-12)y = 0

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Q: A 6-ft man walks away from a 16-ft high lamp post at the rate of 4 ft/s.  How fast does the tip of…

A: Given that, A 6-ft man walks away from a 16-ft high lamp post at the rate of 4 ft/s.

Q: 5. Given z = arctan (), Find az/ay

A: We can find the partial derivative wrt y as below.

Q: Question 5 Which of the following is not true? A None of the given choices ℗ √ ² in(x²) dx = I'm √…

A: The objective is to find which option is not true.

Q: Write TRUE or FALSE before each statement. Solve y' - ³y = dependent variable. differential…

A: