Describe the difference between the explicit form of a function and an implicit equation. Give an example of each.
> Use implicit differentiation to find an equation of the Show that the equation of the tangent line to the ellipse
> Explain why the derivative of x2 + y2 + 2 = 1 does not mean anything.
> Find the derivative of the function.
> Write two different equations in implicit form that you can write in explicit form. Then write two different equations in implicit form that you cannot write in explicit form.
> Find an equation of the tangent line to the graph at the given point. Kappa curve
> Find an equation of the tangent line to the graph at the given point. Lemniscate
> Find an equation of the tangent line to the graph at the given point. Astroid
> Find an equation of the tangent line to the graph at the given point. Cruciform
> Find an equation of the tangent line to the graph at the given point. Circle
> Find an equation of the tangent line to the graph at the given point. Parabola
> Folium of Descartes: x3 + y3 - 6xy = 0 Find the slope of the tangent line to the graph at the given point.
> Find the slope of the tangent line to the graph at the given point. Bifolium: (x2 + y2)2 = 4x2y
> Find the slope of the tangent line to the graph at the given point. Cissoid: (4 - x)y2 = x3
> Find the derivative of the function.
> Find the slope of the tangent line to the graph at the given point. Witch of Agnesi: (x2 + 4)y = 8
> x cos y = 1, (2, π/3) Find dy/dx by implicit differentiation. Then find the slope of the graph at the given point.
> tan(x + y) = x, (0, 0) Find dy/dx by implicit differentiation. Then find the slope of the graph at the given point.
> x3 + y3 – 6xy – 1, (2, 3) Find dy/dx by implicit differentiation. Then find the slope of the graph at the given point.
> (x + y)3 = x3 + y3, (-1, 1) Find dy/dx by implicit differentiation. Then find the slope of the graph at the given point.
> Find dy/dx by implicit differentiation. Then find the slope of the graph at the given point.
> Find dy/dx by implicit differentiation. Then find the slope of the graph at the given point.
> 3x3y = 6, (1, 2) Find dy/dx by implicit differentiation. Then find the slope of the graph at the given point.
> xy = 6, (-6, -1) Find dy/dx by implicit differentiation. Then find the slope of the graph at the given point.
> (a) find two explicit functions by solving the equation for y in terms of x, (b) sketch the graph of the equation and label the parts given by the corresponding explicit functions, (c) differentiate the explicit functions, and (d) find dy/dx implicitly
> Find the derivative of the function.
> (a) find two explicit functions by solving the equation for y in terms of x, (b) sketch the graph of the equation and label the parts given by the corresponding explicit functions, (c) differentiate the explicit functions, and (d) find dy/dx implicitly
> (a) find two explicit functions by solving the equation for y in terms of x, (b) sketch the graph of the equation and label the parts given by the corresponding explicit functions, (c) differentiate the explicit functions, and (d) find dy/dx implicitly
> (a)find two explicit functions by solving the equation for y in terms of x, (b) sketch the graph of the equation and label the parts given by the corresponding explicit functions, (c) differentiate the explicit functions, and (d) find dy/dx implicitly
> Find dy/dx by implicit differentiation.
> y = sin xy Find dy/dx by implicit differentiation.
> cot y = x - y Find dy/dx by implicit differentiation.
> csc x = x(1 + tan y) Find dy/dx by implicit differentiation.
> (sin πx + cos πy)2 = 2 Find dy/dx by implicit differentiation.
> sin x + 2 cos 2y = 1 Find dy/dx by implicit differentiation.
> x4y – 8xy + 3xy2 = 9 Find dy/dx by implicit differentiation.
> Find the derivative of the function.
> x3 – 3x2y + 2xy2 = 12 Find dy/dx by implicit differentiation.
> Find dy/dx by implicit differentiation.
> x3y3 – y - x = 0 Find dy/dx by implicit differentiation.
> x2y + y2x = -2 Find dy/dx by implicit differentiation.
> x3 – xy + y2 = 7 Find dy/dx by implicit differentiation.
> 2x2 + 3y3 = 64 Find dy/dx by implicit differentiation.
> x5 + y5 = 16 Find dy/dx by implicit differentiation.
> x2 - y2 = 25 Find dy/dx by implicit differentiation.
> x2 + y2 = 9 Find dy/dx by implicit differentiation.
> How is the Chain Rule applied when finding dy/dx implicitly?
> Find the derivative of the function.
> Explain when you have to use implicit differentiation to find a derivative.
> In your own words, state the guidelines for implicit differentiation.
> Let k be a fixed positive integer. The nth derivative polynomial. Find Pn (1)
> Let f(x) = q1 sin x + a2 sin 2x + ∙ ∙ ∙ + an sin nx, where a1, a2, . . ., an are real numbers and where n is a positive integer.
> Determine whether the statement is true or false. If it is false, explain why or give an example that shows it is false. If y is a differentiable function of u, u is a differentiable function of v, and v is a differentiable function of x, then.
> Determine whether the statement is true or false. If it is false, explain why or give an example that shows it is false. If y is a differentiable function of u, and u is a differentiable function of x, then y is a differentiable function of x..
> Determine whether the statement is true or false. If it is false, explain why or give an example that shows it is false.
> The linear and quadratic approximations of a function f at x = a are P1 (x) = f’(a)(x - a) + f(a) and P2 (x) = ½ f’’(a)(x - a)2 + f’(a)(x - a) + f(a). (a)Find the spec
> f(t) = (9t + 2)2/3 Find the derivative of the function.
> The linear and quadratic approximations of a function f at x = a are P1 (x) = f’(a)(x - a) + f(a) and P2 (x) = ½ f’’(a)(x - a)2 + f’(a)(x - a) + f(a). (a)Find the spec
> f(x) = |sin x| Use the result of Exercise 114 to find the derivative of the function. Answer: f(x) = |sin x|
> h(x) = |x| cos x Use the result of Exercise 114 to find the derivative of the function. Answer: h(x) = |x| cos x
> f(x) = |x2 - 9| Use the result of Exercise 114 to find the derivative of the function.
> g(x) = |3x - 5| Use the result of Exercise 114 to find the derivative of the function.
> Let u be a differentiable function of x. Use the fact that
> Show that the derivative of an odd function is even. That is, if (-x) = -f(x), then f’(-x) = f’(x). Show that the derivative of an even function is odd. That is, if (-x) = -f(x), then f’(-x) = f’(x).
> Find the derivative of the function g(x) = sin2 x + cos2 x in two ways. For f(x) = sec2 x and g(x) = tan2 x, show that f’(x) = g’(x).
> Let r(x) = f(g(x)) and s(x) = g(f(x)), where f and g are shown in the figure. Find (a) r’(1) and (b) s’(4).
> Let f be a differentiable function of period p. Is the function f′ periodic? Verify your answer. Consider the function g(x) = f(2x). Is the function g′(x) periodic? Verify your answer.
> Find the derivative of the function. g(x) = 3(4 – 9x)5/6
> Consider the function f(x) = sin βx, where β is a constant. Find the first-, second-, third-, and fourth-order derivatives of the function. Verify that the function and its second derivative satisfy the equation f″(x) + β2 f(x) = 0. Use the results of pa
> The value V of a machine t years after it is purchased is inversely proportional to the square root of t + 1. The initial value of the machine is $10,000. Write V as a function of t. Find the rate of depreciation when t = 1. Find the rate of depreciation
> The number N of bacteria in a culture after t days is modeled by Find the rate of change of N with respect to t when t = 0, (b) t = 1, (c) t = 2, (d) t = 3, and (e) t = 4. (f) what can you conclude?
> The cost C (in dollars) of producing x units of a product is C = 60x + 1350. For one week, management determined that the number of units produced x at the end of t hours can be modeled by x = -1.6t3 + 19t2 – 0.5 t – 1
> The normal daily maximum temperatures T (in degrees Fahrenheit) for Chicago, Illinois, are shown in the table. Use a graphing utility to plot the data and find a model for the data of the form T(t) = a + b sin(ct - d) where T is the temperature and t is
> A buoy oscillates in simple harmonic motion y = A cos ωt as waves move past it. The buoy moves a total of 3.5 feet (vertically) from its low point to its high point. It returns to its high point every 10 seconds. Write an equation describing the motion o
> A 15-centimeter pendulum moves according to the equation θ = 0.2 cos 8t, where θ is the angular displacement from the vertical in radians and t is the time in seconds. Determine the maximum angular displacement and the rate of change of θ when t = 3 seco
> The displacement from equilibrium of an object in harmonic motion on the end of a spring is /
> The frequency F of a fire truck siren heard by a stationary observer is Where ±v represents the velocity of the accelerating fire truck in meters per second. Find the rate of change of F with respect to v when The fire truck is approaching
> The graphs of f and g are shown. Let h(x) = f (g(x)) and s(x) = g( f (x)). Find each derivative, if it exists. If the derivative does not exist, explain why. Find h’ (3) Find s’ (9)
> y = 5(2 – x3)4 Find the derivative of the function.
> Describe the Chain Rule for the composition of two differentiable functions in your own words.
> Tawana owns and operates a sole proprietorship and has a 37 percent marginal tax rate. She provides her son, Jonathon, $8,000 a year for college expenses. Jonathon works as a pizza delivery person every fall and has a marginal tax rate of 15 percent. a)
> Cloud computing is the use of hosted computer facilities through the Internet. Gmail, RIA Checkpoint, and even your iPhone are some applications of cloud computing. a) If HP provides a customized bundle of servers, storage, network and security software,
> Winkin, Blinkin, and Nod are equal shareholders in SleepEZ, an S corporation. In the conditions listed below, how much income should each report from SleepEZ for 2019 under both the daily allocation and the specific identification allocation method? Refe
> Owl Vision Corporation (OVC) is a North Carolina corporation engaged in the manufacture and sale of contact lenses and other optical equipment. The company handles its export sales through sales branches in Belgium and Singapore. The average tax book val
> Sandra would like to organize BAL as either an LLC (taxed as a sole proprietorship) or a C corporation. In either form, the entity is expected to generate an 8 percent annual before-tax return on a $500,000 investment. Sandra’s marginal income tax rate i
> Spartan Corporation, a U.S. corporation, reported $2 million of pretax income from its business operations in Spartania, which were conducted through a foreign branch. Spartania taxes branch income at 15 percent, and the United States taxes corporate inc
> Nicole’s employer, Poe Corporation, provides her with an automobile allowance of $20,000 every other year. Her marginal tax rate is 32 percent. Poe Corporation has a marginal tax rate of 21 percent. Answer the following questions relating to this fringe
> This year, Jolt Inc. reported $40,000 of taxable income before any charitable contribution deduction. Jolt contributed $10,000 this year to Goodwill Industries, a public charity. Compute the company’s current E&P.
> On May 1, year 1, Anna received 5,000 shares of restricted stock from her employer, Jarbal Corporation. On that date, the stock price was $5 per share. On receiving the restricted stock, Anna made the 83(b) election. Anna’s restricted shares will all ves
> Marcus is the CEO of publicly traded ABC Corporation and earns a salary of $1,500,000. Assume ABC has a 21 percent marginal tax rate. What is ABC’s after tax cost of paying Marcus’s salary?
> Cathy, Heathcliff, and Isabelle are equal shareholders in Wuthering Heights (WH), an S corporation. Heathcliff has decided he would like to terminate the S election. In the following alternative scenarios, indicate whether the termination will occur and
> What tax benefits does the buyer hope to obtain by making a §338 or §338(h)(10) election? Describe how this election might affect the value offered for the target corporation.
> Describe the three hurdles a taxpayer must pass if he wants to deduct a loss from his share in an S corporation. What other loss limitation rule may impact the deductibility of losses from an S corporation?
> Describe the advantages (if any) of using a reverse triangular form of Type A reorganization in acquiring other corporations.
> Lauren is 17 years old. She reports earned income of $3,000 and unearned income of $6,200. Is it likely that she is subject to the kiddie tax? Explain.
> Gerry (age 56) and Elaine (age 54) have been married for 12 years and file a joint tax return. The couple lives in an apartment in downtown Manhattan. Gerry’s father, Mortey, recently retired from Del Boca Vista Corporation (DBVC), where he worked for ma
> While James Craig and his former classmate Paul Dolittle both studied accounting at school, they ended up pursuing careers in professional cake decorating. Their company, Good to Eat (GTE), specializes in custom-sculpted cakes for weddings, birthdays, an
> Abigail, Bobby, and Claudia are equal owners in Lafter, an S corporation that was a C corporation several years ago. While Abigail and Bobby actively participate in running the company, Claudia has a separate day job and is a passive owner. Consider the
> Barry Potter and Winnie Weasley are considering making an S election on March 1, 2020, for their C corporation, Omniocular. However, first they want to consider the implications of the following information: • Winnie is a U.S. citizen a
> Ray and Chuck own 50 percent capital and profits interests in Alpine Properties LLC. Alpine builds and manages rental real estate, and Ray and Chuck each work full time (over 1,000 hours per year) managing Alpine. Alpine’s debt (both at the beginning and
> Until the end of year 0, Magic Carpets (MC) was a C corporation with a calendar year. At the beginning of year 1 it elected to be taxed as an S corporation. MC uses the LIFO method to value its inventory. At the end of year 0, under the LIFO method, its
