1. Find the average rate of change for the following functions over the given intervals. a) f(x)=4x-2x²+3x between x=-1 and x=4 b) y lnx between x=1 and x=4

Q: 1. how do i find the value at which f is discontinuous and is f continuous from the right, or from…

A: Step 1:Step 2:Step 3:Step 4:

Q: Question Determine lim f(x) given the definition of f(x) below. (If the limit does not exist, enter…

A: I have solved the problem and given the answer with proper steps and explanation. Kindly check it…

Q: GUIDED PRACTICE Apply the laws of exponents in each. 1. (4a³b²)(-2a²b²)2

A: The given expression is (4a3b2)(-2a2b2)2.

Q: 2. Let f(x) = 2x² + 6. Find and completely simplify the rate of change on the interval [3,3+h]. (5…

A: We find the rate of change of f(x) = 2x2 + 6 on the interval [3, 3 + h] by using the formula for the…

Q: #70

A: We evaluate the integral:  ∫x3x4−6x2−7​dx  Step 1: Simplify the integrand Divide each term in the…

Q: 5 2 3. f(x) = 3x3 - 15x3 Find the intervals of increasing, decreasing 4. If xy+cos y, Find

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Q: Is the function f(x) continuous at x = 1? (z) 6 5 4 3. 2 1 0 -10 -9 -7 -5 -2 -1 0 1 2 3 4 5 6 7 8 9…

A: *The function f(x) is continuous at x = 1-> This is the correct answer since the function is…

Q: The answer is A Show me how to do it

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Q: Please help on all asked questions. Please show all work and steps. Please circle the final answer.

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Q: In this project, you will use spreadsheet software (either Microsoft Excel or Google Sheets, please)…

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Q: = Let (6,2,-5) and = (5,4, -6). Compute the following: บี.บี. บี. นี = 2 −4(u. v) = (-4). v= ū.…

A: Given vectors:u=⟨6, −2, −5⟩,v=⟨5, 4, −6⟩. Thank you   Alternative solution: Given vectors:u=⟨6, −2,…

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A: Note :  we have formulas,  a⋅ba×b​=∣a∣⋅∣b∣cosθ=∣a∣⋅∣b∣sinθ​ where, θ is the angle between the two…

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Q: 3. Evaluate. Leave your answer in simplest exact form: 8 x²+x+1 √x dx

A: Step 1:

Q: find the general soultion (D-DxDy-2Dx)Z = sin(3x+4y) + x²y

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Q: please solve problem 4. Thank you

A: (b) Solve the differential equations provided in (a) for Rt.To solve the differential equation for…

Q: 2. Find the function f(x) given that f'(x) = 3cos (x) - 2sin(x) and f(π/6)=√3. Leave your answer in…

A: To find the function f(x), we need to integrate f'(x). f′(x)=3cos(x)−2sin(x) Integrating both sides,…

Q: Please help on all asked questions. Please show all work and steps. Please circle the final answer.

A: i) The planes are coincident:For planes to be coincident, they must be scalar multiples of each…

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A: If you have any questions let me know in the comment box thankyou.

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Q: Please find the power series representation of h(x) as well as the IOC. You can use table of…

A: Step 1: Power series of tan−1(x) From the Maclaurin series table:…

Q: For number 9 The answer is A Could you show me how

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Q: j) f) lim x+x ex g) lim Inx h) lim x-5 i) lim arctan x x700 lim arctanx 811x

A: Final Answers: (f)limx→∞​exx​=0. (g)limx→∞​lnx=∞. (h)limx→∞​x−5=0. (i)limx→∞​arctanx=2π​.…

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A: Step 1:Step 2:Step 3: Step 4:

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A: Now we can calculate sin(3A)By substituting the values :- sin(3A) = sin(3 * 25/8) ≈ -0.162…

Q: #39

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Q: • • Let > be a potential for the vector field F = (−2 y³, −6 xy² − 4 z³, −12 yz² + 4 2). Then the…

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Q: Let m(t) be a continuous function with a domain of all real numbers. The table below shows some of…

A: The given table of m(t) is :tm(t)​−3−7​−26​83​11−9​120​​(a) Given point is (−3,−7). This means…

Q: Solve the initial value problem: y= 0.05y + 5 y(0) = 100 y(t) =

A: We are solving the initial value problem: dtdy​=0.05y+5,y(0)=100.  This is a first-order linear…

Q: Example(1): (Adiabatic humidification and cooling of air). Air has to be humidified and cooled…

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Q: = (2² +²+2)/2/2 dV, where D is the region in the first octant By changing to spherical coordinates,…

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Q: The correct answer is D Could you please explain why

A: Given the vector field: F(x,y,z)=(y−z2+2x3,−z+x2+2y3,x−y2+2z3)We need to compute the outward flux of…

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A: Approach to solving the question: Detailed explanation:Examples: Key references:

Q: Differentiate #32, #35

A: Step 1:Step 2:Step 3:Step 4:

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A: Step 1: Define w Step 2: Compute p(w)Step 3:Roots of p(x) Step 4: Final Answer

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Q: 4 HW/ os x ex dx 2X 3 6054x dx

A: Step 1: Step 2: Step 3: Step 4:

Q: 3. Differentiate the following functions. Show your work where applicable. a) y = e³x b) f(x)=2…

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Q: Find the following limit lim x-4 X-72 3x-6

A: We need to evaluate the limit:limx→2​3x−6x2−4​ Step 1: Substitute x = 23(2)−622−4​=6−64−4​=00​Since…

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A: Step 1: Step 2: Step 3:Step 4: Given step-by-step solution. if any clarification is required do…

Q: Ministry of Higher Education & Scientific Research Babylon University College of Engineering - Al…

A: Q1 uses the power series method where we assume a solution in the form of an infinite series and…