Calculus question and answers for October 18, 2023
- Q Find the derivative.f(x) = sinh-(-9x)f'(x) =
- Q Use differentials to estimate the amount of paint needed (in m) to apply a coat of paint 0.04 cm thick to a hemispherical dome with diameter 56 m. (Round your...
- Q If x + y + z = 9, dx/dt= 8, and dy/dt =5, find dz/dt when (x, y, z) = (2, 2, 1).
- Q Find the derivative, r'(t), of the vector function.r(t) = a + 5tb + tc
- Q Use substitution to determine whether the given x-value is a solution of the equation.tan x =?3/3, x= -5?/6YesNo
- Q (a) Find the unit vectors that are parallel to the tangent line to the curve y = 8 sin(x) at the point (?/6 ,4).smaller i-componentlarger i-component(b) Find the unit vectors...
- Q Find f'(x) and find the values(s) of x where f'(x) = 0.f(x) = (2x - 45) (x +168)f'(x) =x=(Type an integer or a simplified fraction. Use a comma to separate...
- Q An investment of $9,000 earns interest at an annual rate of 8.5% compounded continuously. Complete parts (A) and (B) below.(A) Find the instantaneous rate of change of the amount in...
- Q Find (A) the derivative of F(x)S(x) without using the product rule, and (B) F'(x)S'(x). Note that the answer to part (B) is different from the answer to part (A)-F(x) =...
- Q Find the equation of the line tangent to the graph of f at the indicated value of x.f(x)= 8+ Inx; x = 1
- Q Creamy Bugs Yogurt has found that the cost, in dollars per pound, of the yogurt it produces, is C'(x) = -0.003x + 450, for x ? 300, where x is...
- Q Use the chain rule to find dz/dtz = xy^9 - x^2y, x = t^2 + 1, y = t^2 - 1
- Q Find f(x+h) - f(x) / h for the function f(x) = 10x - 9
- Q Determine the angle between 0 and 2? that is coterminal to 1020.
- Q Let (u, v) be the inner product on R generated by A = [4 1] [-2 1]and let u = (0, -2), v = (4,2). Find (u, v).(u, v) =Current...
- Q Let f(x) = |x|-2 Evaluate the function at the given values. Then select the appropriate graph that represents this function.a. f(-2) = Type your answer hereb.f(-1) = Type your answer...
- Q Consider the following.3/x - 1/y =7(a) Find y' by implicit differentiation.y' =(b) Solve the equation explicitly for y and differentiate to get y' in terms of x.y' =(c) Check that...
- Q Find dy/dt for each pair of functions.y=x-7x, x = t +3
- Q Find the derivative of the following function.A = 690(1.702)^t
- Q Find an exponential function of the form P(t)= Pon^1/T that models the situation, and then find the equivalent exponential model of the form P(t)=Poe. Doubling time of 4 yr, initial...
- Q Differentiate the function.f(x) = x(x + 4)f'(x) = 4x + 12x
- Q Find the derivative of the function.f(t)- 7t sin(ut)
- Q Find dy/dx by implicit differentiation.x - 14xy + y = 14
- Q Let f(u) = u and g(x)=u=6x^5 +5. Find (fog)'(1).(fog)'(1) =(Type an exact answer.)
- Q Find dy/dt for each pair of functions.y=x-2x, x= t +4dy/dt=
- Q The demand for a new computer game can be modeled by p(x) = 41-8 In x, for 0 ?x? 800, where p(x) is the price consumers will pay, in dollars,...
- Q Use the chain rule or general power rule to determine the derivative of the followingf(x)=(2x-6x)^ 32.) y=?6x +8
- Q For the polynomial below, -1 is a zero.f(x)=x - 5x + 6Express f(x) as a product of linear factors.
- Q Find all ercepts and y-intercepts of the graph of the function.f(x) = 2x +9x+10If there is more than one answer, separate them with commas.Click on "None" if applicable.x-intercept(s): 0y-intercept(s): 0None0/0Xx0/60,0....S0/6?
- Q - 23x + 48x6Determine the intervals on which f is decreasing.Consider f(x)Of is decreasing on:Of is decreasing nowhere.Determine the intervals on which f is increasing.Of is increasing on:Of is increasing...
- Q Consider h(y) = -7 cos y +7?3 siny on [0, 2?].Determine the intervals on which h is decreasing.Oh is decreasing on:Oh is decreasing nowhere.Determine the intervals on which h is...
- Q Find the derivative of the function.f(x) = sin(6
- Q Find all critical numbers of the function g(x)=x-14x.O critical numbers: x=0, x=?14, x= -?14O critical numbers: x=0, x=??7, x= -?7O critical numbers: x = ?14, x =O critical numbers: x...
- Q Find the relative extremum of f(x)=-3x +30x+8 by applying the First Derivative Test.
- Q Complete two iterations of Newton's Method for the function using the given initial guess.f(x) = x - 4? x? = 1.1
- Q Find the marginal revenue function.R(x) = 3x -0.04xR'(x) =
- Q Find the derivative of the function.f(?) = cos(?)f'(?) =
- Q Find y" by implicit differentiation. Simplify where possible.x + 3y =3y" =
- Q Find dy/dx by implicit differentiation.tan(x - y) =y/2+x
- Q 1. Which of the following statement is false? (a) d/dx In(2x) = d/dx In(x) for x > 0. (b) d/dx csc(x) = cot(x) csc (x) for x = (0, ?)....
- Q Find the equation of the tangent line tof(x) = 1 + eX + X2at x = 0.
- Q Find the total change of f(x) between x = 1 and x = 4, when df/dx =1/x1.250.750.25-0.75
- Q let f(x) = sin x. Write an expression for f(x) using the definition of the derivative, but don't evaluate the limit.
- Q If the number of fruit flies F increases at a rate that is proportional to the number of flies present, write the differential equation that describes the rate of change...
- Q The interest on an account increases exponentially.If an initial investment of $5000 earns $900 in two years, what is the rate of increase at the end of that second year?A....
- Q Let g(w) = -arctan(17^w)Determine the critical values of g. If multiple such values exist, enter the solutions using a comma-separated list.
- Q Let h(y) = 10y - 5Determine the critical values of h. If multiple such values exist, enter the solutions using a comma-separated list.
- Q Let g(z)=5ze^3zDetermine the critical values of g. If multiple such values exist, enter the solutions using a comma-separated list.
- Q Let h(w) = -3.8?w?Determine the critical values of h. If multiple such values exist, enter the solutions using a comma-separated list.
- Q Let g(v) = -6v + 18v +7 - 16vDetermine the critical values of g. If multiple such values exist, enter the solutions using a comma-separated list.
- Q Let f(u) = -14u(u + 10)1/3Determine the critical values of f. If multiple such values exist, enter the solutions using a comma-separated list.u =No critical values exist.
- Q Find dy/dx by implicit differentiation.x^2/ x+y= y + 8
- Q Let g(x)=x?9+10xDetermine the critical values of g. If multiple such values exist, enter the solutions using a comma-separated list.x = No critical values exist.
- Q Find the derivative of the function.f(x) = (2x - 6)^4(x + x + 1)^5
- Q Find the derivative of the function.f(t) = 5t sin(nt)f'(t) =
- Q Finddy/dx by implicit differentiation.x sin(y) + y sin(x) = 1dy/dx=
- Q Find dy/dx by implicit differentiation.x-18xy + y = 18
- Q Find dy/dx by implicit differentiation.xe^y = x-ydy/dx=
- Q Find the derivative of the function.F(t) = e^8tsin(2t)F'(t)=
- Q Find the derivative of the function.y = e^tan(?)y' =
- Q Find the derivative of the function.f(z) = e^z/(z - 9)
- Q Find dy/dt using the given values.y = x - 4x for x = 5, dx/dt = 3.dy/dt=
- Q Find the derivative of the function.F(x) = (9x^6 + 8x)^4
- Q Find the derivative of the function.f(x) = ?3x + 4f'(x) =
- Q Use the implicit differentiation to find the derivative dy/dx= y', given the implicitequations:e^3xy = 3x + y
- Q Find the derivative of the function.h(t) = (t + 3)^2/3 (2t - 1)h'(t) =
- Q Find dy/dx by implicit differentiation.y cos(x) = 4x + 5yy' =
- Q Find f.f'(t)= sec(t)(sec(t) + tan(t)),- ?/2 < t < ?/2, f(?/4)=-1
- Q For the given composite function, identify the inner function, u = g(x), and the outer function, y = f(u). (Use non-identity functions for f(u) and g(x).)y = tan(?x)(f(u), g(x)) =...
- Q Two trains leave from the same station, one going north at 30 miles/hr and one going west at 40 miles/hr. The one going west leaves 1 hour later than the...
- Q Find the first and second derivative of the function.G(r) = ?r + ?r
- Q If R4) 13 and f'(x) z 2 for 4 ? x ? 6, how small can f(6) possibly be?
- Q The function p(t) = 2000t/ 4t+75 gives the population p of deer in an area after t months.a) Find p'(5), p'(25), and p'(50).b) Find p''(5), p''(25), and p''(50).c) Interpret the...
- Q The equation of motion of a particle is s= t - 27t, where s is measured in meters and t is in seconds.(a) Find the velocity and acceleration as functions...
- Q Consider the following.Find f'(x).f'(x) =f(x) = x5 - 4x + x-1Compare the graphs of f and f' and use them to explain why your answer is reasonablef'(x) = 0 when...
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