Calculus question and answers for October 24, 2023
- Q Let g(x) = log3(x+5) + 3Determine the derivative of g- at x = 4.(g-)'(4) =
- Q Question 16feet per second<A 6 foot tall woman walks at a rate of 6 feet per second toward a lamppost that is 15 feet tall.Determine the rate of change of...
- Q Find x where 0 ? x ? ?.3 tanx = secx - tanx
- Q Suppose and y are both differentiable functions of t andxy = ? 8Determinedydt=dydt"dxdtgiven = 6, 7, and y = 6.=
- Q Let g(x) =2x + 4Determine the derivative of g- at x = 2.(g-) '(2) =-
- Q Suppose and y are both differentiable functions of t andy =- 3x + 6x - 2Determine dy / dt given dx/dt =2 and x=8dy/dt=
- Q Let h(v) = arcsin ( - 5v)Determine the derivative of h.h'(v) =Determine the slope of h at v = 0.h'(0) =
- Q Let f(y) = arctan6(5)Determine the derivative of f.Determine the slope of f at y = -7.f'(-7)=
- Q Let g(x) = 9?x - 5Determine the derivative of g- at x = 18.(g-) '(18) =
- Q Let g(v)arccsc (e7v)Determine the derivative of g.=g'(v) =Determine the slope of g at v = 12.g'(12) =
- Q Let g(x) = 2 sin x on?2? x ?FINDetermine the derivative of g at x = ? 1.(g-) '(-1) =
- Q Let g(z)= z^2 /3 +10 cos(z) +e^z +10 sin(z)Determine the third derivative of g.d^3 z/dz=
- Q Let h(x) = x + 7x + 6Determine the derivative of h- at x = 14.(n-) '(14) =
- Q Let f(x) = (x+8) +8, for x > - 8.Determine the derivative of f- at x = 12.(f )'(12) =
- Q Divide.(12x + 30x+12) + (2x+4)Your answer should give the quotient and the remainder.
- Q Let f(w) = 11^w + log?11 (w^8)Determine the derivative of f.f'(w) =
- Q Let g(x) =x + 8/x+2Determine the derivative of g- at x = 3.(g-) '(3) = |
- Q Let f(x) = arcsec (e-2)Determine the derivative of f.f'(x) =Determine the interval(s) on which f is differentiable. Report the solution using interval notation.f is differentiable on
- Q Let h(t) = arccos (9t7)Determine the derivative of h.h'(t) =-63t6V1-81t14Determine the slope of h at t = 0.h'(0) =0
- Q Let g(y) = arctan(- 9y)Determine the derivative of g.g'(y) =Determine the slope of g at y = -6.g'(- 6) =
- Q Let f(x) = 7 3?x-7+2Determine the derivative of f- at x = - 12.(f-) '(- 12) =
- Q Let f(x) = 7+2Determine the derivative of f at x = 9.(-) '(9) =
- Q ConsiderDetermine the derivative of y with respect to a.y = 42y6 sin (6y7) +3+ xy = coscos (6y7)
- Q (7)4Determine the derivative of f.Let f(v) = - 7arctan (f'(v) =Determine the slope of f at v= - 2.f'(-2) =
- Q Let f(t)= = arccos (?4t)Determine the derivative of f.f'(t) =Determine the interval(s) on which f is differentiable. Report the solution using interval notation.f is differentiable on
- Q Cliff divers on an exotic island dive off cliffs that are 59 meters above the sea. The position of a diverabove the sea at time t is given by s(t)...
- Q Suppose both f and f- are differentiable functions such that f(5) = 3913Determine (f) (3).(-) '(3) = f'(5) ==
- Q Let f(x) =9Determine the derivative of f.f'(x) = -(9)(x)3GDetermine the interval(s) on which f is differentiable. Report the solution using interval notation.f is differentiable on (-?,0) u (0,00)
- Q Let h(u)DetermineDu[h(u)]4e" tan(u)D [h(u)]
- Q Let f(x) =9Determine the derivative of f.f'(x) =Determine the interval(s) on which f is differentiable. Report the solution using interval notation.f is differentiable on
- Q Let h(x) = x + 9x - 3Determine the derivative of h - at x = 7.(h-) '(7) =
- Q 3 + xyDetermine the derivative of y with respect to x.=os (6y7)COS
- Q Let f(x)8arctanMinDetermine the derivative of f.f'(x) =Determine the interval(s) on which f is differentiable. Report the solution using interval notation.f is differentiable onx
- Q Let f(a)P9Determine the derivative of f.f'(x) =Determine the interval(s) on which f is differentiable. Report the solution using interval notation.f is differentiable on
- Q Let g(u) =- 10u/?u-6Use logarithmic differentiation to determine the derivative of g.d/du[g(u)]=
- Q Let h(t) = arccos (9t)Determine the derivative of h.[Determine the slope of h at t = 0.h'(0) =h'(t) =
- Q Let f(x) = e5 + coss (?117)4Determine the derivative of f.f'(x) =Determine the slope of f at x = 6.f'(6) =
- Q Let h(x) = x - 15x + 4.Use either of the limit definitions of the derivative to differentiate h.h'(x)=Determine the slope of h at x = 7.h'(7) ==
- Q An object's velocity after t seconds is v(t) = 26 2t feet per second.(a) How many seconds does it take for the object to come to a stop (velocity =...
- Q Find a function f such that f '(x) = 5x and the line 135x + y = 0 is tangent to the graph of f.=
- Q Find the derivative of the function.sin(2x)f(x)cos(9x)
- Q Use Newton's method with the specified initial approximation x? to find x3, the third approximation to the solution of the given equation. (Round your answer to four decimal places.)2-x+1=0,x?-2==X
- Q Consider the function below.f(x) = -3x + 6x + 6Exercise (a)Find the critical numbers of f.Step 1Differentiate f(x)=-3x + 6x + 6 with respect to x.f'(x)==SubmitSkip (you cannot come back)Exercise...
- Q Explain why Newton's method doesn't work for finding the root of the equationx 3x + 1 = 0if the initial approximation is chosen to be x? = 1.f(x) = x...
- Q Find all relative extrema of the function. Use the Second Derivative Test where applicable. (If an answer does not exist, enter DNE.)36Xf(x) = x +relative maximumrelative minimum(x, y) =(x, y)...
- Q ASK YOUR TEACHERDetermine whether the Mean Value theorem can be applied to f on the closed interval [a, b]. (Select all that apply.)f(x) = 16x + 31, [-1,3]Yes, the Mean...
- Q The amount of garbage, G, produced by a city with population p is given by G = f(p). G is measured in tons per week, and p is measured inthousands...
- Q Find all values of 0 (in rad) that satisfy the equation over the interval [0, 2?].sin(---)sin(0) = sinsmaller valuelarger value8 =0==radrad
- Q Find each limit, if it exists.2 - 9xX-? 2x-8(a) lim(b)(c)2 - 9xlimX- 2x - 8=112 - 9xlimx18 2x - 811
- Q Consider the following function.f(x) = x - 4x(a) Find the critical numbers of f. (Enter your answers as a comma-separated list.)X=(b) Find the open intervals on which the function is...
- Q This question has several parts that must be completed sequentially. If you skip a part of the question, you will not receive any pointsfor the skipped part, and you will...
- Q Use Newton's method with initial approximation x? = -1 to find x?, the second approximation to the root of the equation x3 + x + 8 = 0. (Round your...
- Q Simplify.sinx secx - secx
- Q Use the Table of Integrals to evaluate the integral. (Use C for the constant of integration.)" arctan(vx)new window?x
- Q Consider the following relation.{(-2, 2), (0, 5), (1, 6), (1, 7), (2, -1), (3, 1))A. Is it a function?B. Is it a one-to-one function?
- Q What is the amplitude ofy = cos x?[?]
- Q Let f be the function given by f(x)=x-3x. What are all values of c that satisfy the conclusionof the Mean Value Theorem of differential calculus on the closed interval [0,3]?OA)...
- Q Let f be a function defined and continuous on the closed interval [a,b]. Iff has a relativemaximum at c and a<c<b, which of the following statements must be true?I. f'(c)...
- Q Convex quadrilateral ABCD has AB = 6, BC = 7, CD = 9, and DA = 5. The area ofquadrilatearl of ABCD is 30. Determine the exact value of cos(ZDAB-ZBCD).
- Q Perform the following operations onthese complex numbers.(2-1)(1+3i)
- Q Use a system of linear equations with two variables and two equations to solve. A moving company charges a flat rate of $80, and anadditional $5 for each box. A...
- Q Let f (x) = 4x - xf(x+h)-f(x)hEvaluateO 8x +4h-1O 8x +4h+1O 8x +4h-1-2O 8x +4h+1O4h-12x04h-1-2/22xand simplify.
- Q Let g(v) = v^14vUse logarithmic differentiation to determine the derivative of g.d/dv[g(v)]=Determine the slope of g at v = 1.g'(1) =
- Q Let f(x)= x(x ? 4)^8/(x + 2)^6Use logarithmic differentiation to determine the derivative.f'(x) =
- Q Use implicit differentiation to determinedydxdydxgiven the equation a + y = ? 3.P
- Q A rocket is launched vertically upward with an initial velocity of 29 ft/sec. Its height hin ft above the ground after t seconds can be represented by the following equation.How...
- Q (v + 3) (v + 7)(v-7)(v-2)Use logarithmic differentiation to determine the derivative of f.Let f(v) =dv[f(v)]=
- Q Let g(y) = (y + 1) (y + 3) (y 9)Use logarithmic differentiation to determine the derivative of g.Dy[g(y)]=
- Q 9u(u + 3) (u + 2)Use logarithmic differentiation to determine the derivative of f.dduLet f(u)=-[f(u)]=
- Q Convert thefollowing equationinrectangular form topolar form.A. r sin 0 = 2B. r cos 0 = 2C. r = 2x = 2D. cos 0 = 2
- Q The function f(x) =is increasing on the open interval (4x + 15x + 435.12z - 6.05It is decreasing on the open interval (-?,The function has a local maximum at) and...
- Q Let h(w) = wln (15w)Use logarithmic differentiation to determine the derivative of h.Dw[h(w)]==
- Q Consider the function f(z)-5-47, -5 ? ?2The absolute maximum value isand this occurs at z =The absolute minimum value isand this occurs at x =
- Q Solve the rational equation and identify the solution set.6-x-612-3-242O a) {30}20Ob) {-2, 3}000d) {6}
- Q Given the equation below, finddydx=y =dydx24x7 + 9x6y + y = 343Now, find the equation of the tangent line to the curve at (1, 1). Write your answer in mx...
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