3 2. xdy + y = xy²³ ху dx

Q: Suppose that a fourth order differential equation has a solution y = - =-6e5x (a) Find such a…

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Q: Find y' if 7 y² + sin (3x) = 12-yf

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Q: 1. We are interested in evaluating the integral 3 [√9-2² dr. Note that this integral gives you the…

A: Given: ∫039-x2dx a ) Let fx = 9-x2 Using Riemann sum with 3 rectangles and right-hand endpoints we…

Q: For the function below, find a) the critical numbers, b) the open intervals where the function is…

A: A point x=a is said to be a critical point of f(x) iff f'(a)=0

Q: hat values of p does 8 Sx 1 Pdx converge? I the correct choice below and, if necessary, fill in the…

A: We have to find the value of p for divergence according to the given information

Q: Rewrite the quadratic function f(x) f(x)= ■ Vertex: = 2x² + 4x + 7 in standard form, f(x) = a(x -…

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Q: Suppose lim n ---> infinity is known to exist, lim n---> bn= 5, lim n---> bn an ^2  = 245 find lim…

A: Given:- limn→∞bn=5  limn→∞bnan2=245

Q: Determine all equilibrium solutions and classify as stable, semi- stable, or unstable. dx dt a. b.…

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Q: 1+tan^2x/sec^2x-sinxtanx/secx-cos^2x

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Q: Prove the identities sinh(2x)=2sinh(2)cosh(2)

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Q: Find the transform of the given function by use of a table. f(t) = 3e-4t sin 5t (A) F(s)- (B) There…

A: We need to find Laplace transform.

Q: If a snow ball melts so that its area decreases at a rate of lcm³/min, find the rate at which the…

A: The rate at which the area of the snow ball changing is dAdt = -1 cm2/min To evaluate: The rate at…

Q: A graph is defined by the equation x²-√3xy + 2y² = 12. Part A: Find dx Part B: Find the equation of…

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Q: Quantitatively prove the following: If f: R3 → R  has continuous second derivatives, then  ∇ × (∇f)…

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Q: If a rock is thrown vertically upward from the surface of Mars with velocity of 25 m/s, its height…

A: The given data is: h=25t-1.86t2 Initial velocity u=25 m/s (a) To find the velocity of rock after 4 s…

Q: 0 = XP(^vx-2)^x + ^p (Tvx-tv^) differential equations.

A: A differential equation of the form Mdx+Ndy=0 is exact if ∂M∂y=∂N∂x, and general solution is…

Q: Classify the following DE's as Exact, Non-exact, Homogeneous or Bernoulli. A: (-xysinx + 2ycosx) dx…

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Q: Are 2 -baz

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Q: ind y" if y tan x. A] 2sec²x tan x D] 2 sin x + 2 cos x [B] secx tan x [E] sec x tan²x [C] 2 cos x…

A: y=tan(x)    ddx(  tanx ) = sec2x

Q: Obtain the differential equation of this family of curves. The lemniscate ² = acos 20

A: see below the answer and calculation

Q: Find the inverse transform of the given function of s. F (s)- -4s2 - 6 (s+ 4Xs +6Xs-7)

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Q: If an arc has a length of 3 does this cover an angle less or more than 180 degrees and why?

A: We need to describe arc length.

Q: x + 3y s 18 2x + yΣ 14 x Σ Ο Υ Σ Ο

A: See this solution in below.

Q: Use logarithmic differentiation to find the derivative of the function. y = (In(x)) cos(9x) y'(x) =…

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Q: . Evaluate the for parametric equations x = 3t² - 6t and dx = 3t³ + 3t with respect to the…

A: Given query is to find the Indicated derivative.

Q: Find the equation of the plane tangent to the surface G(x,y,z)=2x^2+y^2+3z^2=25 at P=(−3,−2,1).

A: Topic = Derivative

Q: answer

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Q: Determine if the improper integral is convergent or divergent, and calculate its value if it is…

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Q: 1. Determine the equations of the tangent and normal lines at P(1,1) given x³y - 2xy² + x² - 3y + 3…

A: To determine the equations of tangent and normal to the given curve.

Q: 2 Evaluate the following Integral - Find the partial fraction decompe √x3-3x² dx =

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Q: Calculate the consumer's surplus at unit price ō = 10 for the demand equation q=20 -0.05p²

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Q: Question 3 Find the transform of the given function by use of a table. f(t) = e4t 1 (A) F(s)= S + 4…

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Q: Find y' @ (1.1) if

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Q: Let y = f(x) = 6x³ + 13x - 13 and g the inverse function of f. Note that f(1) = 6. Find the value of…

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Q: Find by implicit differentiation. dx 2x sin(xy³) = x +2y-7

A: As we know that; The Sum/Difference rule: f±g'=f'±g' The Power law: ddxxn=nxn-1 The Product rule:…

Q: Give the appropriate form of the partial fraction decomposition for the following function. 5x (x -…

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Q: Consider the following autonomous first-order differential equation. y' = y² + 2y 1194994 ++ + + +

A: Given differential equation y'=y2+2y

Q: Consider the following integral. Sketch its region of integration in the xy-plane. 0 LL 9-x² 6xy dy…

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Q: xis that the terminal position of the angle resides in and state the value of the reference angle.…

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Q: [(x² +1) cos +=dx 2

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Q: 5) Use the Integral Test to determine whether the series below converges or diverges. a) State why…

A: The objective is to solve the above question.

Q: An object thrown vertically upward from the surface of a celestial body at a velocity of 12 meters…

A: Solution ) s(t) = -6t2 + 12t  Differentiate  with respect to t  s'(t) = - 6 × 2t + 12  [ formula…

Q: 3. Let f(t) = t(1 - 2t). a) Find the average rate of change of f(t) with respect to t as t changes…

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Q: The independent variable x is missing in the given differential equation. Proceed as in this example…

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Q: Suppose that a population of bacteria triples every hour and starts with 300 bacteria. Find an…

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Q: Concept Check: Evaluate the following integrals: e³x dx 1-2e³x 2. ·S₁ TENTIA

A: To evaluate the given integral.

Q: Let Find dy || ¹. y = f(x) = arcsin In 7x. dy dx

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Q: Find the derivative of y = 3x² − 2x + dy = 6x 2 dx dy dx dy dx Oy = = 3x - 1 = 3x - 2 6x - 2

A: Given query is to find the derivative of the function.

Q: √x² ²-4 .3 x -dx

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Q: Find the derivative. 1 y = _x3 + 3x + Væ 2 Ody dx O Ody dx || ip O 32 y=2x2 +3 + 2x 32 || 2 X +3+1/x…

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