Fill in the blanks: The derivative of a product of two functions is the first function times the of the second plus the second function times the derivative of the first. < Previous Continue >

Q: Find the given limit. 2 X -5 lim 4-x X -4 x -5 lim %D 4 -x X→ -4 (Simplify your answer.)

A: Find the given limit

Q: 1 erivative of x²+2

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Q: Related Rates A rock is thrown into a still pond. The circular ripples mové outward from the point…

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Q: Let -1 <r< 1, the series r na" is the power series representation of the n-1 function

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Q: Evaluate the limit x2+19x- 48 lim x--3 x2-11x+42 O a. а. 0 b. None of these. С. 13 11 d. 00 е. 13 17

A: Limits

Q: PERFORMANCE TASK 1. The population of a city years from now can be modeled by the function P(x) =…

A: Concept: Graph: A graph is a graphical representation of data that is organized on a graphing plane…

Q: if f'f′ is the derivativeof ff with 2∫1f'(x)dx=10∫12f′(x)dx=10 and f(2)=4,f(2)=4, then f(1)

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Q: 1) Find the hundredth derivative of p (x) = (x+ x³ + x")1º (1 + x²)!' (x³ + x³ + x7). Justify your…

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Q: x-16 x'+8 The function f(x)=D- has derivatives f'(x)= 48 and f"(x)=- 10 (d) Determine the intervals…

A: Given problem:-

Q: 11. Write true if the statement is correct and false if the statement is incorrect. Given the…

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Q: Find an equation of the tangent line to the graph of x* + 3xy? + y = 15 at the point (1, 2).

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Q: Let C be the cost to produce x batches of widgets, and let Rix) be the revenue in thousands of…

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Q: A power representation of the function f(r) = for -1<r<1i %3D 1+z Select one: 00 8n n-0

A: Given Rewrite where  a = 1

Q: Find the Taylor series of  f(x)=ln(2+x) around the point x=-1 by reaching the term n=4

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Q: Given the function f(x) = -x* - 4x determine its critical points and classify them, determine the…

A: We have to find the points and check the nature of function.

Q: I. Find the general solution of the following: dy 2x 1.- dx y dy 2. xy dx 3. dy = (6e3x+ 1)dx

A: We have to find the general solution.     According to our guidelines we can do only one question so…

Q: Suppose that a cylindrical can is designed to have a radius of 1 in. and a height of 5 in b the…

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Q: x’y? If z , show that x=+ y- 3z x+ y ôx ây a²z ô²z = 0 if z= Tan 2.xy x² – y? Show that âx² ' ây²

A: A detailed solution is given below.

Q: Given (x+ y}* – ( x - v}² = x* + y^, find dy/dx using implicit differentiation. A. - 2- E. None of…

A: Given x+y2-x-y2 =x4+y4. We have to find dydx  using implicit differentiation.

Q: The volume of the solid of revolution obtained by revolving the region enclosed by the x-axis and…

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Q: Find the slope of the tangent line to the curve (a lemniscate 2 (a² + y²)° = 25(x² – y²) at the…

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Q: Find the volume of the solid obtained by rotating about the y-axis the region bounded by y=x² and…

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Q: 5. Use Linear Approximation to estimate e(-0.01). Show work

A: answer is in next step

Q: Write a in the form a = a-T+anN at the given value of t without finding Tand N. r(t) = (2t + 3)i +…

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Q: ² f r' రy2 Əx? dy? dz? x² + y? + z²

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Q: A Norman window is constructed by adjoining a semicircle to the top of an ordinary rectangular…

A: Here we have to use the concept of derivatives.

Q: Solve the initial value problem for r as a vector function of t. dr Differential equation: = - 22k…

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Q: 4. Find the volume of revolution generated by revolving the region between f(x) = 9-3x and f(x) =…

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Q: A power representation of the function f(r) = for -1 <a<1 is 1+ %3D

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Q: Find the area of the region between the curves y = 12 – a? and y = x² – 6. Area between curves =

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Q: II. Find the area bounded by each of the following curves. Show your complete solution. Write your…

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Q: Find the limit. Answer in either fraction or integer form. NO DECIMAL APPROXIMATIONS. If the limit…

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Q: Write the sum 5 + 15 + 45+ + 1215 using sigma notation. ... a1(1 – r") - Then evaluate the sum using…

A: Solve the following

Q: 7. Let f(x) - -ar + 9x -3. a. Determine thex-values where f"(x) = 0. b. Fill in the table below to…

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Q: 9. Find the vertical and horizontal asymptotes of the function. X-8 f(x): х2 — х — 6

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Q: Given the triangle 13 find the length of side x using the Law of Cosines. Round your final answer…

A: This question is related to Triangles, we will solve it using given information.

Q: f'(x)=-+e2* +x² and S(1) =. Find f(x) Given %3D

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Q: 7. Find the exact x-value where the function f (x) = x + In (p² – 1) attains a maximum value. An…

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Q: Σ Preview i=1

A: We will use sigma notation.

Q: Let -1 <a < 1, the series r na" is the power series representation of the n-1 function Select one:…

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Q: 24 2. 3. 25 Equation: Solution: Ec So Triple?. Tr Triple Family: . Tr

A: According to company rule we can answer only first question and rest can be reposted.

Q: 2. A boat is being pulled into a dock by a rope attached to it and passing through a pulley on the…

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Q: ,11,,11 x"yll The expression log can be written in the form 24 A log(x) + Blog(y) + C log(z) where A…

A: logmn=log(m)-log(n) log(m.n) =log(m)+log(n) logmn =n log(m)

Q: 11. (e* sin y – 3x²)dx + ( e* cos y+ |dy = 0 12. (2x + 1+x?y? ) dx +( -29) dy = 4 - 29) dy = 0…

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Q: (ii) Prove the identity (2 - 2 cos 0) (sin 0 + sin 20 + sin 30) -(cos 40 - 1) sin 0 + sin 40 (cos 0…

A: Since the student has posted multiple questions and does not mention any specific question, so we…

Q: x - 2x +4x–8 Draw a graph of the function R(x) = Justify all major features using limits. x -11x+18

A: To solve the following problem

Q: A volleyball is hit when it is 4 ft above the ground and 12 ft from a 6-ft-high net. It leaves the…

A: We need to find vector form.

Q: Find the arc length parameter along the curve from the point where t= 0 by evaluating the integral s…

A: Arc length

Q: A tire swing attached to a tree branch swings with an arc length of 40 feet on its first swing. On…

A: Question- A tire swing attached to a tree branch swings with an arc length of 40 feet on its first…

Q: Find the number(s) b such that the average value of f(x) = 6x2 - 42x + 70 on the interval (0, 6 is…

A: Use formula for average value of function .