eliminate the arbitrary constant y= x^2+C1e^2x+C2e^3x

Q: Find the distance in netween the point P(-4,3,-1) and Q(4,-1,3)

A: given points P(-4,3,-1) Q(4,-1,3)formula for distance is D=(x2-x1)2+(y2-y1)2+(z2-z1)2

Q: Use the Trapezoidal Rule, the Midpoint Rule, and Simpson's Rule to approximate the given integral…

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Q: Find the volumes of the solids generated by revolving the triangle with vertices (2,2), (2,7), and…

A: The volumes of the solids generated by revolving the triangle with vertices (2,2), (2,7), and (5,7)…

Q: Find the area of the region enclosed between f(x) = x² − 3x + 3 and g(x) = 2x² – 3x – 1. Area =…

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Q: graph the equation y=-3/4x-5?

A: Given query is to graph the equation.

Q: Find the distance from the point S(5, -6,6) to the line x = 10t, y = 6t, and z = 7t. The distance is…

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Q: Find r(t) if r'(t) = t² i + et j + 3te³t k and r(0) = i + j + k.

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Q: Question 19 >D Next If you know that f(x) = f'(x) = f'(x) and that f(-4)= 3 while f(-2) = 3e² then:…

A: here we have to find the integral.

Q: Find the directional derivative of f(x,y,z)=-4x2+2y2-3z2 at the point (1, 4, 5) in the direction of…

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Q: 2. Let f(x,y) = x2 + y xy³ (a) 0 (b) 1 (c)-1 (d) 1/2 (e) Does not exist. Find lim (x,y) →(0,0) f(x,…

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Q: 7. Evaluate the limit or explain why it does not exist. (a) (b) (c) lim (x,y)-(2,-1) lim (x,y) →…

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Q: Suppose a company has fixed costs of $300 and variable cost per unit of x +1460 dollars, where x is…

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Q: Question 6 Solve the DE. If (x) is the solution to the DE, find (-2) y'=xe}-x’; y(0) =0 0.675 -0.675…

A: To solve the DE. If ϕx is the solution to the DE, the to find ϕ-2. y'=xey-x2; y0=0

Q: Given: z = x² + xy², x = uv² + w³, y=u+ve™ Find when u = -2, v = 1, w=0 Əz Əv

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Q: Estimate the value of the limit (if it exists) by evaluating the function at the given numbers. (It…

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Q: Consider the ellipsoid 3x2+2y2+z2=12. The implicit form of the tangent plane to this ellipsoid at…

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Q: Solve the following differential equation. Show your complete solution. 2. x² dx + y(x - 1)dy

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Q: Solve the following differential equation. Show your complete solution. 1. (1-x)y' = y².

A: (1-x)y'=y2(1-x)×dydx=y2dyy2=dx(1-x)∫yndy=yn+1n+1+c∫1xdx=lnx+c

Q: The production of a gold mine decreases by 5% per year. What is the approximate half-life for the…

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Q: s dx √x-1 +√x+1

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Q: Problem 9 dy dx = x+y-4 3x + 3y - 1

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Q: Find for In (7y) = e sin (2x). dy dx dy =

A: ln7y=eysin(2x)d dx(lnx)=1xd dx(sinx)=cosxd dx(ex)=exd dx(a.b)=adbdx+bdadx

Q: The force F on an object is the product of the mass m and the acceleration a. In this problem,…

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Q: The equation y'-y=4te is a first order linear DE in standard form. True O False

A: The objective is to find the correct option .

Q: Use the limit definition of the derivative to find the slope of the tangent line to the curve f(x) =…

A: Given query is to find derivative and the slope of the tangent.

Q: dr Find for 0-718 de de || -7/8 -r = -3. -

A: Given query is to find indicated derivative.

Q: The force F on an object is the product of the mass m and the acceleration a. In this problem,…

A: F(t)=m(t)a(t) at t=7 s,  m(t)=51 gramschanging rate=m'(t)=9 gsat t=7, a(t)=8 ms2  changing…

Q: Solve 2 cos² (w) - cos(w) - 3=0 for all solutions.

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Q: Prove that AC B if and only if A U B = B

A: To prove:- A⊂B if and only if A∪B=B

Q: Find the error in the following work. Dx 2x+5 = = = (2x+5)(2x) - (x²-1) 2 (x²-1)² 4x² +10x-2x² +2…

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Q: Find all relative maxima and minima of the following function. 1(x) = 4x³ - 3x² - 6x +17 f(x) has a…

A: Second derivative test for maxima and minima :  Consider the function f(x) Find critical point f'(x)…

Q: se Simpson's Rule with n = 10 to estimate the arc length of the curve. Compare your answer with the…

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Q: rate

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Q: 5. Define g(x)=7dt a. Evaluate g(x) for x=2, 4,6, 8, 10. Plot the five points on g(x) which are…

A: Given data :  Define  g(x)=∫t=1t=x 1tdt

Q: 4 Ssinª 3xdx

A:

Q: lim [f(x) - g(x)] x→2 lim_[f(x) - g(x)]= [ X→2 (Simplify your answer.)

A: given limits are :-limx→2f(x) = 22 and      limx→2g(x)=8then we have to evaluate the following limit…

Q: 2a + bx Ex B f(x)=√√2a @f(x) = 3ax-5 x+b f(x) = 32²³ +26 ×-5c x-5c, a÷0

A: f'(x) = limh->0 f(x+h) - f(x)h This is the definition of derivative using limit.

Q: Select any necessary conditions for a function to be differentiable over its domain.   Question…

A: We know that a smooth function is a function that has continuous derivatives up to some desired…

Q: Given the function P(x)= x³5x² - 24x, find its y-intercept is its x-intercepts are 1 X1 < x2 < 3…

A: Given function:- Px=x3-5x2-24x

Q: Find the mass, the moments, and the center of mass of the solid E with the given density function p.…

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Q: 6. y 1=1/√2², y = , y = 5 - x²; about the x-axis 4

A: Topic = Volume

Q: When demonstrating that lim suffices? 8=0.000004 = 0.000001 ✓=0.000002 1 = ∞ with M = 100000, which…

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Q: The directional derivative of z = f(x, y) at (1,5) in the direction toward the point (7, 4) is 17…

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Q: Find the volume of the solid obtained by revolving the region in the first quadrant bounded by y =…

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Q: 3. Use (shortcut) rules of derivatives to find f'(x) a. f(x) = 15x²-3x5 + c. f(x) = x³ + 2x²-9x+5 X…

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Q: Consider the following function. Answer f(x) = x - Step 1 of 2: Find the slope and the y-intercept.…

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Q: 6 Suppose fƒ(¹) da = -2 and f g (x) dx = 9. 4 4 Evaluate (4 f (x) + 2 g(x)) da. 4 Remember to…

A: Introduction: Integration is a way of uniting the part to find a whole. In the integral calculus,…

Q: A piece of cardboard measuring 12 inches by 11 inches is formed into an open-top box by cutting…

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Q: -50x7 - 30x6 - 20 5x² Type your answer without negative exponents. Simplify completely. Find the…

A: Given the quotient function is -50x7-30x6-205x2

Q: Evaluate f 5x√3+25x² Show ALL work clearly. If using the table of integrals for this problem, be…

A: Concept: Integrating the components into the whole is the process of integration. In the integral…