Calculus question and answers for October 23, 2023
- Q Consider the differential equation=y-t.dyIs each of the following a solution to y - t?Select true or false for each proposed solution.y=t+2 [Select]y=t+1 [Select]y=t+1+2et [Select]
- Q 8) y =(? / + 6) (3x ?+4)xdifferentiate the function-2
- Q Find an equation of the tangent line to the graph of fat the given point.f(x) = ??x, (9, 3)y =
- Q Find the derivative of f(x) = 3?x -9a 10/2x8.Type your answer without fractional or negative exponents. Use sqrt(x) for ?.'(x) =
- Q Suppose that the position of a particle is given by s = f(t) = 2t + 6t+ 9.(a) Find the velocity at time t.v(t) =(b) Find the velocity at time...
- Q Find the derivative of f(x)==- 4?x6x4Type your answer without fractional or negative exponents. Use sqrt(x) for ?.f'(x) =
- Q This exercise uses the radioactive decay model.The half-life of radium-226 is 1600 years. Suppose we have a 23-mg sample.(a) Find a function m(t)= mo2-/h that models the mass remaining after...
- Q Use the product rule to find the derivative of(-3x0 + 5x)(7e - 7)Use e^x for et. You do not need to expand out your answer.
- Q Simplify the expression (3i + 2)(1 - i).O-i-1O i +5Oi-12
- Q If f(x) = 3x ? 7x + 6, find '(1).-Use this to find the equation of the tangent line to the parabola y.= 3x - 7x + 6 at the...
- Q Find the accumulated present value of an investment over a 7 year period if there is a continuous moneyflow of $5,000 per year and the interest rate is 1.2% compounded...
- Q If f(x)f'(x) =='(4) =5 sin x2 + cos xthen
- Q Let f(x) = 2x + 14 - 3e. Then the equation of the tangent line to the graph of f(x) at the point(0, 11) is given by y = mx...
- Q Use the quotient rule to find the derivative of5e + 64x0 - 6xUse e^x for e. You do not need to expand out your answer. Be careful with parentheses!
- Q Find the vertical asymptotes of the rational function y = 2-16XOx= 0 and x = 1Ox= 1 and x = -1Ox=4 and x = -4y = 4 and y =...
- Q Let f(x)x + 8.Find the values of a where f'(x) = 7.Give exact answers (not decimal approximations).The greater solution is x =The lesser solution is =
- Q If g(x) = 1 - 2x + 3x2, find the average rate of change of the function as xvaries from 2 to 5.19253360
- Q If f(x)'(x)=-3x sin x cosa, findFind f'(4) =
- Q y = (4x + tan(x)) dydxFinddydx=Type sin(x) for sin(x), cos(x) for cos(x), and so on.Use x^2 to square x, x^3 to cube x, and so on.Use (sin(x))^2 to square sin(x).
- Q If f(x) =f'(x) =' (2) =2 sin xI3 + cos xthen
- Q Radio stations in a certain country use a sequence of 5 or 6 letters as their station identification call letters. The first letter must be W, N, C, Q, or...
- Q (10 points) If f(3) = 8, f'(3) = 4, g(3) = 2, g'(3)=-6, find F'(3) if F(x)=?f(x) g(x)
- Q Let f(x) =4x + 14if x < -2?x+38 if x > - 2if x = - 22limH12Select all statements below that you agree with.Note: You may be checking more than...
- Q Use the product rule to find the derivative of(10x5 + 2x)(8 + 9)Use e^x for e. You do not need to expand out your answer.
- Q Let u(x) = sin(x) and v(x) = x and f(x)u'(x) =v'(x) =f' =u'v - uv'v==u(x)v(x)
- Q Find the derivative of the functiong(x) = (5x ? x-1) eg'(x) =-
- Q If f(x)f'(x) =f'(2) =5x(sin x + cos z), find
- Q DetermineOy = log; (x + 1)dydx(T+1) In 321(T+1)(7+1) In 320(T+1)21for the following function:
- Q (1) Which is the correct formula for finding the derivative of the product of two functions?(fg)' = f' + g'O(fg)' = fg' + gf'(fg)' = f'g'(2) Use the correct formula...
- Q Let f(x)HoMINIMAThen f'(x)b-|9 sin r2 sin x + 6 cos xThe equation of the tangent line to y = f(x) at x = 0 can be written in the form...
- Q Given the function: f(x)1.) (a) Find: f(-4)11-3x5x + 2, find the following functional values.(b) Find: f(3)
- Q If f(x)'(x)==5x sin x cos x, findFind '(1) =
- Q Find the derivative of:f(x) = x(1 - x)O (1 - x)(1 - 3x)2(1-x)O (1 - x)(-1 - x)O-2 (1-x)
- Q Letf(x) = 9 cos x + 3 tan x'(x) =-f'(57)3=
- Q Determinedydxat x=-2 for y = 3u + 2u and u =?x + 5.
- Q If f(x)f'(x) =-f'(2) =4 sin x2 + cos x7then
- Q y = xe 2x 0 ? x ? In3On this interval, the maximum value(s) occur at x =In3120O two of the above are correctShy
- Q Find the derivative of f(x) = 7?x3x10#Type your answer without fractional or negative exponents. Use sqrt(x) for ?.'(x) =
- Q Differentiate y =O0OO2?x 4x2?x +1A? ?x + ?212?x + ??/x?x + ?x
- Q In(x-3) < 0 if and only ifOx< 4Ox> 3Ox>403<x< 400<x<0 < x < 4
- Q If f(x)= ex, which of the following lines is an asymptote to the graph of f?Oy=xOy=0Oy = -xOy=1O x = 047
- Q y = (6x + 3) y = (6x + 3) 5Let y =Finddydxdy dydx dxdydaType sin(x) for sin(x)sin(x), cos(x) for cos(x) cos(x), and so on.Use x^2 to square x, x^3...
- Q y =Finddydx(2x + 9e) dydxType sin(x) for sin(x), cos(x) for cos(x), and so on.Use x^2 to square x, x^3 to cube x, and so on.Use (sin(x))^2 to square sin(x).A
- Q A cell culture contains 2 thousand cells, and is growing at a rate of r(t) = 6e0.00t thousand cells per hour.Find the total cell count after 3 hours. Give your...
- Q Find the derivative of the function g(x) =g'(x) =e5 - 4x
- Q What is the modulus of the conjugate of (2 + 3)?O ?13O ?15O?5O?3
- Q y =Finddydx(9x + cot(x))7dydx||Type sin(x) for sin(x), cos(x) for cos(x), and so on.Use x^2 to square x, x^3 to cube x, and so on.Use (sin(x))^2 to square sin(x).
- Q Find dy/dx by implicit differentiation.(?os ?x + sin ??) = 13dy/dx =
- Q Find the derivative of f(x) = f(x) = 7?x - ?3x10310TType your answer without fractional or negative exponents. Use sqrt(x) for ???.f(x) = f'(x) =
- Q Solve csc (5x) - 7 = 0 for the four smallest positive solutionsC =
- Q Considery + In(xy) = 2Determine the equation of the tangent line at (e, 1). Report the solution using slope-intercept form.
- Q (1) If f(x) = x, then f'(x) =(2) If g(x) =(3) If h(x) =- 5x4, then g'(x) =1x5'then h'(x) =
- Q Let h(w) = -6 sin (2?w)Determine the value(s) of w on (0, 1), if any, for which h has a horizontal tangent line. If mulitple such valuesof w exist, use...
- Q Let g(x) = 5e7x - 6Determine the derivative of g.g'(x) =Determine the slope of g at x = 4.g'(4) =
- Q Let f(x)Determine=- 7 cos( - 2x)the derivative of f.f'(x) =Determine the slope of f at x = 7.'(7) ==
- Q Use the definition of derivative to find f'(x) and f(x).f(x) = 5x + 6x +3f'(x) ==
- Q Find dy/dx by implicit differentiation.(4x + 4y) = 64x + 64y,dydx=At (-1, 1): y' =Then find the slope of the graph at the given point.(-1, 1)
- Q Consider-4 ln(y) = 5y sin xDetermine the equation of the tangent line at (0, 1). Report the solution using slope-intercept form.Submit Question
- Q Let h(y) = ln (y(y + 1) )Determine the derivative of h.dhdy
- Q Finddydxdydxwhereye-5x 9x - y = 8-
- Q Consider-9x5 +7x6y + y = ? 1Determine the derivative of y with respect to x.y'Determine the equation of the tangent line to the curve at (1, 1). Report the solution...
- Q Let f(y)=35(y - 3)Determine the value(s) of y, if any, for which f has a horizontal tangent line. If mulitple such values of yexist, use a comma-separated list to enter...
- Q Consider20=(tan(10y) +Determine the derivative of y with respect to x.dydxcsc (6x))8
- Q Consider(sin(8x) + cot (4y))' = 5Determine the derivative of y with respect to x.y' =
- Q Let h(x) = (8x ? 8)Determine the derivative of h.h'(x) =Determine the slope of h at x = 1.h(1) =Submit All Parts
- Q Considerx + 1y 2Determine the derivative of y with respect to x.y'= 34-7
- Q Find the first derivative with respect to x.- 2x - 9y + 7y = 8dydx=
- Q Considerx - y = 18-Determine the derivative of y with respect to x.y' =-
- Q ConsiderDetermine the derivative of y with respect to x.--dydxxy=x + 6Y+4- 3-
- Q Considertan(9x + 5y) = e9rDetermine the derivative of y with respect to x.y'
- Q Let f(x) = x(3x)Determine the equation of the tangent line to f at (5, 20). Report the solution using slope-intercept form.
- Q 6x??+1Determine the derivative of g.Let g(x)g'(x) ==
- Q -7x + 7x + 6Determine the derivative of hLet h(x) =h'(x) =5=+7)
- Q A plane flies 452 miles north andthen 767 miles west.What is the magnitude of theplane's resultant vector?Hint: Draw a vector diagram.[?] miles
- Q Find the first derivative with respect to x.? 13x7 + 1ly7 + 2y = 15dydx
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