In Problems 8-9, use the graph of f to estimate the indicated limits and function values.

Q: Expand: (x + 2y)5.

A: Consider the provided expression, x+2y5 Simplify the provided expression. Apply the binomial theorem...

Q: The cost per unit of producing a product is 60 + 0.2x dollars, where x represents the number o produ...

A: Given, The cost of producing a product daily is 60+0.2x dollars  The price that the company charges ...

Q: Given v = 2i + j, w = 6i + 3j, find projw v. Then decompose v into two vectors, v1 and v2, where v1 ...

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Q: How do I find the domain and range of the attached problem?

A: Givenf(x)=x2+8

Q: Given the functions: f(x) = 8 / (x2 + 4) a. List the vertical and horizontal asymptote(s). b. Find t...

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Q: The first part of a is right but I keep getting the second part of a wrong. Also need help with part...

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Q: A trough has a triangular cross section. The trough is 5 ft across the top, 5 ft deep, and 26 ft lon...

A: To Determine: A trough has the a triangular cross section the tough is 5 ft across the top ,5ft deep...

Q: Use the remainder theorem to find the remainder when​ f(x) is divided by the given x−k.f(x)=3x2-4x+4...

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Q: The radius of a sphere is increasing at a rate of 2 inches per minute. Find the rate of change of th...

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Q: Find the parametric equations of the line r = ⟨1, 2, 3⟩ + t(4, 0, -6⟩.

A: Given: r→=1,2,3+t4,0,-6 for any given vector equation of line r→=a,b,c+tp,q,r, parametric equation o...

Q: A rock is thrown into a still pond. The circular ripples move outward from the point of impact of th...

A: Givenradius of circle=6 feetand drdt=4 feet per minute

Q: Differentiate the function. 8x2 + 8x + 2 y = V X

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Q: The minute hand of a clock is 15 cm long and the hour hand is 12 cm long. How fast is the distance b...

A: Given: The minute hand of a clock is 15 cm long and the hour hand is 12 cm long. To find: How fast i...

Q: Plot the given point (-4, -2)in a rectangular coordinate system.

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Q: Use the given information to find the unknown value.   y varies directly as the cube of x. When x=2,...

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Q: dy Find if dx (² + 7)* 3 5,

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Q: Find the general solution analytically. (Enter your solution as an equation.)

A: given equation is, dydx=-xy

Q: Simplify the ratio of factorials. (8n - 1)! (8n + 1)!

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Q: If you could only learn one approach to solving quadratic equations, discuss which of the approaches...

A: For solving quadratic equations, quadratic formula is the best approach.  Because this approach alwa...

Q: Calculus Question

A: Given:       y=1x,  x=7,x=8  about x-axis.

Q: Hi! Please see attached image for the question, thank you!

A: Given: fx=3+10e-2xgx=3+2ex Solving the above 2 equations 3+10e-2x=3+2exe3x=53x=ln5x=ln53=0.5365  

Q: Cost, revenue, and profit are in dollars and x is the number of units.The average cost of a product ...

A: Cost, revenue, and profit are in dollars and x is the number of units. Given that, the average cost ...

Q: To help plan the number of meals to be prepared in a college cafeteria, a survey was conducted, and ...

A: ACCORDING TO BARTLEBY GUIDELINES, SOLUTION OF ONLY FIRST 3 SUBPARTS WILL BE PROVIDED.  

Q: f(x) = 2ax - bx² + 2ax – b %3D

A: fx=2ax3-bx2+2ax-b Now, simplify the above function, fx=x22ax-b+2ax-b=2ax-bx2+1

Q: You are stationary on the ground and are watching a bird fly horizontally at a rate of 10-. m The se...

A: Consider the given conditions. To make the diagram from the given conditions,    

Q: Let f(x) be the function defirted as x² - 2ax + a² f(x) = (x – b)(x + c)’ where a, b and c are const...

A: Given function,  a, b,c are constants in ℝ.  To find the  Horizontal and  vertical asymptotes of th...

Q: If s = 4/t - 3, then %3D ds dt

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Q: Following the procedure on this page, find the instantaneous rate of change of the function f(x)=x^3...

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Q: x+4 if x2 is continuous at x= 2. Verify all three conditions of continuity and be very clear!

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Q: Evaluate each limit. etx - 1 lim xS0 e - 1

A: The given expression is limx→0e4x-1ex-1

Q: You had $10,000 to invest. You put x dollars in a safe,government-insured certificate of deposit pay...

A: (a) Simplify the algebaric expression0.05x+0.1210,000-x=0.05x+1200-0.12x=-0.07x+12000.07x=1200x=1200...

Q: Consider two parabolas y=x^2 and y=−x^2−1. Find all straight lines that are tangent to both of them.

A: Given parabolas are, y=x2 and y=-x2-1

Q: Use properties of limits to find the indicated limit (as shown). It may be necessary to rewrite an e...

A: Given: limx→12x2-3x+52 for solving given limit, we substitute x=1 in given limit

Q: differentiate y = sin^3(tet^2) and simplify

A:             The given function is y=sin3tet2We have to differentiate with respect to t ddt(y)=ddtsin...

Q: in is [- 12,12]. d the critical points, differentiate the function with respect to x. Use the produc...

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Q: Use the integration capabilities of a graphing utility to approximate the area of the surface formed...

A: Given r=4cos2θ and 0≤θ≤π4 To find the area of the surface formed by revolving the polar equation wit...

Q: 3 Evaluate 7x? dx 1 7 (Hint: f(x) = 72? and F(x) = a*) 3

A: The given integral is: ∫137x2dx Since, 7 is a constant, so take it out side. ∫137x2dx=7∫13x2dx The i...

Q: Use the definition of a limit to show that (i) limx→0 (x^2 + 6x + 9) = 9 (ii) limx→−7 and 1/(x+7)^4 ...

A: Authoring guidelines: ______________________________________________________________________________...

Q: The radius of a sphere is increasing at a rate of 2 inches per minute. Find the rate of change of th...

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Q: Place the correct symbol, < or >, in the blank area between the given numbers. Do not use a ca...

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Q: Vx +1 for 0<x<3 (5-x for 3< x< 5 Let f be the function defined by f (x) = %3D (a) Is f continuous at...

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Q: Solve the inequality, 2x2 + 9x + 4 ≥ 0 and graph the solution set on a real number line.

A: Given: 2x2+9x+4≥0 for solving given inequality we use factorization method

Q: If g(t) = 3t + 2t, find all t for which g'(t) = 0. %3D t = Preview

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Q: Find f', f'', f''' and f (4) for the function. f(x) = x° + 3 + 3x + 1 %3D f'(x) = Preview f''(x) = P...

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Q: Use logarithmic differentiation to expand and differentiate y =(x+4)8 / sqrt x4+9

A: we have given y=x+48x4+9now apply log both sides ,we getlog y=logx+48x4+9=8log(x+4)-12log(x4+9)now d...

Limits

When it comes to calculus, limits are considered to be a very important topic of discussion. The main importance of limit lies in expressing the value of a function as it gets closer to a certain value. Also, limits can help you to understand other topics, such as continuity and differentiability better. In a broader sense, every calculus notion is a limit. Other branches of calculus have also been derived from limits.