Calculus question and answers for October 20, 2023
- Q Create a real-world situation involving bearing angles (pages 633-635), where the solution wouldrequire the use of either the Law of Sines or the Law of Cosines. Include a description of...
- Q State the domain and range for y = sin x, y = cos x, y = tan x. Why is it so important to restrict each of these domains to...
- Q Find the difference quotient f(x+h)-f(x)/h, where h ? 0, for the function below.f(x) = 4x +3 Simplify your answer as much as possible.
- Q Find the difference quotient f(x+?_x) - f(x)/?_x of the given function: f(x) = - 3x + 7x-5
- Q If you want to calculate your take-home pay you will need to determine the amount of taxes that will be taken out of your paycheck. To do this, you will:...
- Q Suppose the cost, in dollars, of manufacturing x items is approximated by the function C(x) = 0.2x+5x+500, for 1?x?1000. If the cost of manufacturing one item can be represented by...
- Q For f(x) = 2x, construct and simplify the difference quotient f(x+h)-f(x)/hf(x+h)-f(x)/h =
- Q Obtain the derivative dy/dx.y = 6x--5x - 10dy/dx=___State the rules that you use. (Select all that apply.)O power ruleO difference ruleO constant multiple ruleO sum rule
- Q Suppose f(x) = 4" and g(x) = -3x - 2. Find a simplified formula for the function:k(x) = g(f(x))
- Q A hot brick is removed from a kiln at 225C above room temperature. Over time, the brick cools off. After 2 hours have elapsed, the brick is 30 C above...
- Q If h(t) = e cos(t), d(t) = cos(t), and h(t) = v(d(t)), what is v(t)?
- Q Let f(a) = [ (7t - 9t4+t3+6t) dtxDetermine the fourth derivative of f.d4f/dx4_______
- Q Write the domain in interval notation.f(x) =X+2/X+4(-?, 4) U (4,00)(-?, -4) U (-4,00)(-?, -2) U (-2, 0)(-?, 2) U (2, ?)
- Q Let f(x) = cx + In(cos(x)). For what value of c is f'(?/4) =9? C=
- Q Find the second-order partial derivatives of the function. Show that the mixed partial derivatives f and fx are equal.f(x, y) = 3x?y + 3y?x
- Q Find fxx fxy, fyx,fand yy for the following function. (Remember, fyx means to differentiate with respect to y and then with respect to x.)f(x, y) = e^4xyfxx =
- Q Find fx and fy.f(x,y) = -7 e^ 5x-7yfx(x,y) =
- Q For the function f(x,y) = e ^5xy, find fx and fy.
- Q Find dy/dx by implicit differentiation.x + 5x+9xy--4dy/dx= 2x-5+9y/2y-9xdy/dx= 2x+5+9y/2x-9ydy/dx=x+5+9y/y-9xdy/dx=2x+5+9y/2y-9xdy/dx=2x+5-9y/2y-9x
- Q Find dy/dx for y=x+2/x-3None of these10/(x-3)0-10/(x-3)2/(x-3)
- Q Find the open interval(s) on which f(x) = -2x + 12x+8 is increasing or decreasing.increasing on (??,6); decreasing on (6,?)increasing on (-?,16); decreasing on (16,?)increasing on (-?, 32); decreasing on...
- Q Differentiate: y = secx + tan xsecx (secx + tan x)tan + sec4x2(secx + tanx)4secx tan xsec4x + tan x
- Q Find the derivative of the function f(x) = x5-9/x4f'(x) = 1+36/x5f'(x)- 1-36/x5f'(x) = 1 + 4/x5f'(x) = 1-9x5f'(x) = 1 + 9/x5
- Q Find the derivative of the function = 8 cos 4xy' = -4 sin 4xy' = -8 sin 4xy' = ?32 sin 4xy = 32 cos 4xy' = -32 cos 4x
- Q Determine a coterminal angle of 660.
- Q For the functiony = ln xon the interval [1, 5], find the number guaranteed by the Mean Value Theorem.x = [?]
- Q Given g(x, y) = x + 3xy + 2yI. Find the domain of the function.II. Evaluate g(2, -1)III. Find ALL second partial derivatives.
- Q Show all work and explain your reasoning to write a formula for a trigonometric function that has the following characteristics:a) The domain is (-?, ?) and the range is [-2,...
- Q Find dy/dx using partial derivatives, given thatx - 2xy + y = 4.Hint: Use the Implicit Function Theorem which uses partial derivatives to find dy/dx
- Q Match the operation on the equation that will eliminate logarithms/exponents in each eqaution.Equation 1: In x = 2Equation 2: log3 (x ? 1) = 6Equation 3: log (x x -...
- Q Compute the following values for the given function.f(u, v) = (4u + 2v) e^uv^2f(0, 1) =f(?1, ? 1) =f(a, b) =f(b, a) =
- Q Find the second-order partial derivatives of the function. Show that the mixed partial derivatives fxy and fyx equal.f(x, y) = x + xy + y + x + y
- Q For the given geometric sequence, find r and write an explicit formula for an.a = {5, 40, 320, 2560,... }
- Q Give the first five terms of the sequence.a? = -34, an = (6 + an?1)(1/2)nGive your answers as fractions; do not round.
- Q Use the method of Lagrange multipliers to minimize the function subject to the given constraint.Minimize the function f(x, y) = x + 25y subject to the constraint xy = 1.minimum...
- Q Luis goes out to lunch. The bill, before tax and tip, was $13.65. A sales tax of 8% was added on. Luis tipped 16% on the amount after the sales...
- Q Find the first partial derivatives of the function.g(u, v) = u - vu +vgu =gv =
- Q Find the indicated partial derivative.f(x, y, z) = exyz4; fxyzfxyz(x, y, z) =
- Q Find the derivative of the function.f(x) = arcsin(8x) + arccos(8x)f'(x) =
- Q Find the derivative of the function.g(x) = 2 arccos x 9g'(x) =
- Q Suppose h(t) = 3t+5 t and k(t) = 5 t - 3. Show that h(t) and k(t) are inverse functions using algebra.
- Q Find the derivative of the function.f(x) = arcsec (2x)f'(x) =
- Q A cook needs 3 cups of vegetable stock for a soup recipe. How much is this in pints? Write your answer as a whole number or a mixed number in...
- Q Please state the definition of the kth Taylor polynomial, p(x), for f(x) at x = a. Please also include the definition using summation notation.
- Q Given f(x, y) = -5x5 - xy + 5y^6, findfxx(x, y) =fxy(x, y) =fyy (x, y) =fyz(x, y) =
- Q The expression cot?-csc ?/cot? simplifies to what expression?-tan?-cot?cos?sec?
- Q Consider the following. (If an answer does not exist, enter DNE.)f(x) = ln(2+ sin(x)), 0?x? 2?Find the interval(s) on which f is concave up. (Enter your answer using interval notation.)Find...
- Q Domain and range from the graph of a quadratic function Write the domain and range using interval notation.(a) domain:(b) range:
- Q The function f(x) = ?2x + 30x - 126x + 5 has one local minimum and one local maximum.This function has a local minimum at x equals _______ with value...
- Q Translate it to make it the graph of y = |x+5| +4.
- Q Let f(x) = (2x ? 1)(x ? 2). Find all the values of x for which f'(x) = 0.Present your answer as a comma-separated list:
- Q For the equation given below, evaluate y' at the point (1, -1).y at (1, -1) =e?+8-e?= 6x+2y
- Q Sketch the graph of the surface (3d)z = sin yy = sin z
- Q Let x (t) = 5 cos(t)and y(t) = 3 sin(t)At t = 1,x(1) =y(1) =dx/dt |t=1 = dy/dt |t=1 = dy/dx |t=1 = tangent slope =speed (1) =
- Q Let f be the function whose graph is depicted below.(a) Sketch the slope field of the equation y'= f(y).(b) Sketch the slope field of the equation y'= f(t).
- Q Determine the equation of the sinusoidal function in the form y = a sin(bx +c)+d. Show how you calculated each value using the given information:Maximum = 13, Minimum = 5,...
- Q The height of a tidal wave approaching the face of the cliff on an island is represented by the equation h(t) = 7.5 cos(2?t/9.5) where h(t) is the height, in...
- Q At which values in the interval [0, 2?) will the functions f (x) = cos 2x + 1 and g(x) = sin x + 2 intersect?
- Q The following table shows the rate of water flow (in L/min) through a dam.t (min) 1 4 7 10 ...
- Q If f(t) = (t + 5t + 3) (7t + 3), find f'(t).Find f'(2).
- Q 2. Implicitly differentiate the following functions.(a) xy = 2x + 1(b) y + xy + x=1+x(c) x + y= 4xy
- Q Use the quotient rule to find the derivative of 3e^x +4 / 8x? - 9x?Use e^x for e^x. You do not need to expand out your answer. Be careful with...
- Q Suppose that the functions q and r are defined as follows.q (x) = x +5r(x)=?(x +3)Find the following.(r.q)(1) =(q.r) (1) =
- Q Let f(x) = 12x + 11 - 3e^x. Then the equation of the tangent line to the graph of f(x) at the point (0,8) is given by y = mx...
- Q A ladder 10 m long is leaning against a wall. If the base of the ladder is sliding away from the wall at the rate of 1 m per second,...
- Q Let y = tan (3x + 3).Find the differential dy when x = 4 and dx = 0.3Find the differential dy when x = 4 and drx = 0.6
- Q Given f(x, y) = - 4x^6 - 5xy^5 + 3y, findfz(x, y) =fy(x,y) =fxx (x, y) =fzy (x, y) =fyz(x, y) =fyy(x, y) =
- Q Consider the function f(x) = 1 - 6x, -5 ? x ? 2.The absolute maximum value isand this occurs at x =The absolute minimum value isand this occurs at x...
- Q A spherical balloon is inflated so that its volume is increasing at the rate of 20 cubic cm per second. What is the instantaneous change in surface area, ds/dt, of...
- Q -8 is a/an. (Check all that applies.)natural numberrational numberreal numberirrational numberintegeris a/an.-3/2 is a/an. (Check all that applies.)real numberintegernatural numberrational numberirrational number
- Q Let f(x)= x^4x .Use logarithmic differentiation to determine the derivative.'(x) ='(1) =
- Q If f(x)=In(e^2x), then f'(x)=A) 2xB) 2e^(-2x)C) 1D) 2E) e^(-2x)
- Q If f(x) = 5 arctan(5x), find f'(x).Find f'(3).
- Q Let f(x) = x^3x. Use logarithmic differentiation to determine the derivative.f'(x)= ______'(1)= ______
- Q Let y =3xFind the change in y. ?y when x =3 and ?x = 0.2 ______Find the differential dy when x = 3 and dx= 0.2___
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