A population is modeled by the differential dP equation dt 0.5P – 0.001p² The population is at equilibrium when P = %3D When the population is greater than the equilibrium population, the population is: O increasing decreasing

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A: Using error function erf(f) . 

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A: The objective is to evaluate the indefinite integral.

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A: Given:  fx=4x  gx=x+5 a) f∘gx   we know that      f∘gx=fgx                     =4gx                 ...

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Q: Determine whether each of the following functions is (a) continuous (b) differentiable 1. f(x) = x² ...

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A: Here, the given function is: f(x)=π2+cos (x)⇒f'(x)=-sin x

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Q: Find the average rate of change of the function f(x) = 7x from x, =0 to x = 3. %3D The average rate ...

A: Use the slope formula to find the average rate of change -  m = y2-y1x2-x1, where x1,y1 and x2,y2 ar...

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A: We have to find sign of f'(x) and f"(x)

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Q: Cosx 3. 3 cos r - 5 d.r, Use z = tanr |

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Q: Q1. Solve the following dy (a). y² + xy³ + (5y² – xy + y³ sin y) = 0. %3| dx

A: Let's find. 

Q: Use sigma notation to write the Taylor series about x = xo for the function. 10 In x; xo = 1 %3| Σ -...

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Q: Consider the following function. S4x + 1, x s 1 f(x) 16 – x², x > 1 %3D

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Q: Use any method to determine whether the series converge. 1 (a) 2 k? + 2k + 1 k=1 This series converg...

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A: We have to find radius is increasing at a rate of and surface area is increase at arate 

Q: (a) The curve with equation y² = x³ + 3x2 is called the Tschirnhausen cubic. Find an equation of the...

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Q: Find the Maclaurin polynomials of orders n = 0,1, 2, 3, and 4 and the find the nth Maclaurin polynom...

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Q: The graph of y = f(x) (solid) and its tangent line at (0, - 5) (dashed) is shown. 10+ 6- 4- 10 -9 -8...

A: Given: The graph of y=f(x) and its tangent line is at (0,-5) (dashed) is shown.  

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A: The given integral,    ∫dyyy8-4

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Q: Total cost is C = 9000 + 4.55q and total revenue is R = 5.30q, both in dollars, where q represents t...

A: Since you have asked multiple part question, we will solve the first 3 part question for you as per ...

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Q: 10. tan'x sec x dx

A: Given query is to find the value of the integral.

Q: skill and solving problems with parabolas. 1. Experiment #1: While bouncing the Infinity Ball, Nikki...

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Q: Зах + b Find the derivative of h(x) Assume a, b and c are | 5c constants. h'(x) = %3D

A: The objective is to find the derivative. 

Q: Suppose that f(x+h) -f(x) = -7hx^2 +1hx - 3h^2x + 7h^2 +7h^3 find f'(x)

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Q: Suppose that a piston is moving straight up and down and that its position at time t sec is given by...

A: Explained below 

Q: 51. Suppose that 1 A = and D = 2 | Find X such that AX = D by (a) solving the associated system of l...

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Q: sinha da 1+cosha

A:     ∫sinhω1+coshωdωLet u=1+coshω.=∫1udu=lnuSubstitute back u=1+coshω=ln1+coshωAdd a constant to the ...

Q: Suppose a 15-foot ladder leans against the side of a house so that the angle of elevation of the lad...

A: The objective is to find the distance of the base of the ladder from the side of the house.

Q: Find ∂U/∂T and ∂T/∂U when ((TU −V )^2)ln(W−UV) = ln(2) at the point (T,U,V,W) = (1,1,2,4).

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Q: 2t+9 dt (t2–14t+46) 2t + 9 2t + 9 dt (t – 7)2 – 3° J[(t – 7)2 – 3]² Option 2 Option 1 2t + 9 dt [(t ...

A: Here, to rewrite the given integral: ∫2t+9(t2-14t+46)52dt...(1)

Q: %23 -2 What is the first derivative of f(xr) = -9(e*)¯² %3D Select the correct answer below: -2x xz-...

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Q: Write the equation of the function g(x) that is transformed from the function f(x) = |x], and whose ...

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Q: Sketch a graph of a function having the given properties. f(2) = 2, f′(2) = 0, f′(x) > 0 on (−∞,2),...

A: the function has the properties,f(2)=2f'(2)=0f'(x)&gt;0 on -∞,2f'(x)&gt;0 on 2,∞f''(x)&lt;0 on -∞,2f...

Q: compute the derivative of f(x)=1−4x^2 at the specific point x=2. Evaluate the limit by using algebra...

A: Given query is to find derivative of the expression using definition.

Q: f(Xo + h) - f(xo) A continuous curve y = f(x) has a vertical tangent at x = x, if lim = 00 or - 0o. ...

A: The solution is given below