3. If f(x) = x2 +10 and g(x)=x-3: (a) Solve for x if f (g(x)) =11?√√√ (b) Determine the domain for f(x) g(x)

A: We are given the homogeneous second-order differential equation:y′′ + 2y′ + y = 0Form the...

A: Step 1: (part a) It is given that the tumour growth rate is For EquilibriaSo, Case 1: V = 0then,...

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A: Step 1: V by Slicing method: Region bounded by y=16x​ and y=16x2​ The region is bounded by above...

A: If you have any problem let me know in the comment section.

A: To solve the initial value problem y'' - 10y' + 25y = 0, y(0) = 1, y'(0) = 3, we'll follow these...

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A: Monotonic Convergence Theorem Statement:A nondecreasing sequence that is bounded above converges to...

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A: Step 1: Understanding the Unit CircleCoordinates: On the unit circle, a point at angle θ has...

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A: Problem 14. Vector fieldF(x,y)=⟨2x, 3y⟩.Step 1: Write down the componentsFx​=2x,Fy​=3yStep 2:...

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A: The given equation is X = 0.95 * ln(x). We need to find the value of x that satisfies this equation....

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A: Answer 1Given Integral:(0.018)T=∫1.53.0​x​A​dxNow, we will solve for...

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A: Identify the Characteristic EquationThe standard form of a second-order homogeneous linear...

A: To derive L'Hôpital's Rule for the indeterminate form 0/0 using the Cauchy Mean Value Theorem,...

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A: Here are a few basic math examples with step-by-step explanations:Thank you Reference:Basic Math...

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A: We evaluate the limit: limn→∞​(n4n3​+2n+25n+3​) Step 1: Simplify the first termThe...

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A: We have given, Two positive numbers x and y such that, x+y=14 Solve for y, y=14−x..eq(i) Now,...

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A: To compute the integral I=∫0π/2​cos(x​)dx, set t=x​​, so x=t2 and dx=2tdt. When x=0 we have...

A: Here is the step-by-step explanation: Step 1: Establishing the Differential Equation:​Newton's...

A: We are given the graph of the derivative f'(x), and required to determine the local minima and...

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A: Problem 25 Vector Field: F=⟨1/2,0⟩ Curve: C:y−x2=1 (Parabola) a. Tangent PointsParameterize C as...

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A: Given Vector Field:F(x, y, z) = ⟨y2 cos x, 2y sin x + e^(2z), 2y e^(2z)⟩We are to:Prove that the...

A: Step 1: Vectors in Polar Form: Vectors are given in the form r(cos θ i + sin θ j), where:r is the...

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A: Two planes are parallel if their normal vectors are proportional, and they are coincident if they...

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A: Given Differential Equation: y′′′ − 2y′′ − 5y′ + 6y = ex + x2 We will use the method of undetermined...

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