Calculus question and answers for October 21, 2023
- Q Let f(x)=9/xUse the limit definition of the derivative to differentiate f.f'(x)= ?Determine the slope of f at x = 11.f'(11)= ?
- Q Hannah invested $32,000 in an account paying an interest rate of 2 % compounded quarterly. Mila invested $32,000 in an account paying an interest rate of 1?% compounded continuously. After...
- Q Let f(x)=9x + 4x.Use the limit definition of the derivative to differentiate f.f'(x) = ?Determine the slope of f at x = 9.f'(9) = ?
- Q Let f(x) = x - 5Determine the equations of two unique tangent lines of f that intersect at (-5, 19). Report solutions using slope-intercept form.y =___y =___
- Q Let h(x)=?x.Use the limit definition of the derivative to differentiate h. h'(x) = ________Determine the slope of h at x = 1.h'...
- Q The limit definition of the derivativeLet g(x) = - 8/x-4Use the limit definition of the derivative to differentiate g.g'(x) = ?Determine the slope of g at x = -8.g'(- 8)...
- Q Let f(x) = -8.Use the limit definition of the derivative to differentiate f.f'(x) = ________________________Determine the slope of f at x = -9.f'(- 9) = ________________
- Q Fit a quadratic function of the form f(t) = c? + c? t+ c? t to the data points (0,7), (1, 8), (2, 3), (3, ?6), using least squares. f(t)...
- Q Part 3: Suppose the field has a length of 6,000 feet. Sally buys fencing to enclose it, but has bought 4 feet too much. Rather than throwing away the extra...
- Q 42)Let f(x)=x-5Determine the equations of two unique tangent lines of f that intersect at (-5, 19). Report solutions usingslope-intercept form.y =y =
- Q Let h(x) = 1/4 x + 5 and f(x) = -1/4 x + dDetermine the equation f such that f is perpendicular to h. Report the solution using slope-intercept form.
- Q Let g(x) = (-x? + 3 - 9x)/xDetermine the derivative of g.g'(x) = _________Determine the interval(s) on which g is differentiable. Report the solution using interval notation.g is differentiable on...
- Q Let f(x)=2/x^1/6Determine the derivative of f. f'(x)=Determine the interval(s) on which f is differentiable. Report the solution using interval notation.
- Q Let h(t) 4t^5 + 5t^4 -6t+ 5tDetermine the derivative of h. h' (t)=Determine the interval(s) on which h is differentiable. Report the solution using interval notation.
- Q Let h(v) = 2v (v? + 5)Determine the derivative of h.h'(v) = ______Determine the slope of h at v = 0.h'(0) = _________
- Q Let h(x) =x^5Determine the derivative of h. h'(x) =Determine the interval(s) on which h is differentiable. Report the solution using interval notation.
- Q Let h(x) =1/x^12Determine the derivative of h. h'(x) =Determine the interval(s) on which h is differentiable. Report the solution using interval notation.
- Q maximum and minimum values using Lagrange multipliers.Of all points (x, y, z) that x + 4y + 3z=21, find the one that minimizes (x-1) + (y-1) + (z-1).The given function...
- Q Let g(x)=6/?x. Determine the derivative of g. g'(x) =[ ].Determine the interval(s) on which g is differentiable. Report the solution using interval notation. g is differentiable on [ ]
- Q Let g(x)=-1/x^4Determine the derivative of g. g'(x)=Determine the interval(s) on which g is differentiable. Report the solution using interval notation.
- Q Let h(x) = x^4 - 7^3Determine the derivative of h. h'(x) =Determine the interval(s) on which h is differentiable. Report the solution using interval notation.
- Q Let f(x) = 6x - 3x + 5Determine 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)=9t^13 -3t^-13Determine the derivative of h. h' (t)=Determine the interval(s) on which h is differentiable. Report the solution using interval notation.
- Q Let f(x)=- 6x^11Determine the derivative of f.f'(x)=Determine the interval(s) on which f is differentiable. Report the solution using interval notation.
- Q Find and simplify each of the following for f(x) = 4x-3.(A) f(x + h)(B) f(x+h)-f(x)(C)(f(x+h)-f(x))/h(Do not factor.)
- Q Let g(x) = 9.Determine the derivative of g.Determine the slope of g at X = 7. g'(7)=
- Q Let h(z) = -5z(?/) - 9z(/) + 7z(/)Determine the derivative of h.h'(z) = ______Determine the slope of h at z = 1.h' (1) = ______
- Q Let f(w)=(-5w-4w^4 +3)/w^1/3Determine the derivative of f. f'(w)=Determine the interval(s) on which f is differentiable. Report the solution using interval notation.f is differentiable on_______
- Q Let h(x) = (5 - 2x - 6x?)/x?Determine the derivative of h.h'(x) = ________Determine the interval(s) on which h is differentiable. Report the solution using interval notation.h is differentiable on...
- Q let g(x)=1/x?. Determine the derivative of g. g'(x) =[? ].Determine the interval(s) on which g is differentiable. Report the solution using interval notation. g is differentiable on[ ?]
- Q Find the relative maximum and minimum values.f(x,y)= e^(6x +6y +9)Select the correct choice below and, if necessary, fill in the answer boxes to complete your choice.A. The function has a...
- Q Let g(v)=-v^(12/5) + (2)v^(7/3)-(7)v^(9/8)Determine the derivative of g. g'(v)=[?]Determine the slope of g at v = 1. g'(1)=[?]
- Q Let f(z) = (5z + 7)(-8z +9)a)Determine the derivative of f. f'(z)=b)Determine the slope of f at z = -2.f'(-2)=
- Q find the Taylor series of each function at the indicated number. Give the interval of convergence for each series.f(x)=x In (1 + x/2) ;x=0
- Q You are constructing a cardboard box with the dimensions 2m by 4m. You then cut equal-size squares from each corner so you may fold the edges. What are the dimensions...
- Q You want to enclose a rectangular region with 450 feet of fencing. Express A(w), the area of the region as a function of its with.A(w)=_________
- Q Find the four second-order partial derivatives for f(x,y)=4x^(7).y^(4)+3x^(5).y^(6).fxx = ___fyy= ___fxy = ___fyx = ___
- Q This problem has two parts.Part 1: In 2069, a virus begins in Boston and spreads in such that the number N of people infected grows exponentially with time t. The...
- Q Consider the curve parameterized by: x =2t^3/2 - 1 and y = 5t.(a.) Find an equation for the line tangent to the curve at t = 1.
- Q Consider the function f(x) = 2x + 3x - 4 on the closed interval [-2, 1].Find the exact value of the slope of the secant line connecting (-2, f(-2)) and...
- Q Which of the following is not a solution to sin x-cos 2x = 0 on the interval [0, 2?)? (a)?/6(b)?/2(c)5?/6(d)3?/2
- Q Let g(y) = (y-6) (y + 8)/(y-7)(y-4)Determine g'(y)g'(y) =
- Q Let h(x) = f(x) g(x) and j(x) = f(x)/g(x)x 1 2 3 4f(x) -5 -3 5 ...
- Q Let g(t) = 1/t?Determine the derivative of g.g' (t) =Determine the interval(s) on which g is differentiable. Report the solution using interval notation. g is differentiable on
- Q Let f(x) = (3x + 3)/(-3-7x)Determine the derivative of f.f'(x) =Determine the slope of f at x = - 4.f'(-4)=
- Q Let g(v) = 4e^v / v-9Determine g'(v)g'(v) =
- Q Let f(y) = (-2+3/y) /y+1Determine the derivative of f.f'(y) =Determine the interval(s) on which f is differentiable. Report the solution using interval notation.f is differentiable on
- Q Let g(w)= [(w+1)/(w-5)]*(8w - 7)Determine g' (w)g' (w)=
- Q Let f(v) = 9-v / 1-vDetermine the derivative of f.f'(v) =Determine the interval(s) on which f is differentiable. Report the solution using interval notation.f is differentiable on
- Q Let g(x) = x {5+ 2/(x-5)}Determine the derivative of g.g'(x) =Determine the slope of g at x = -2.g'( - 2) =
- Q If f(x) and g(x) are continuous functions and c(x) = f(g(x))use the table below to evaluate c'(-2).x f(x) g(x) ...
- Q Let h(u) = (6u + 8) (-3u + 8) (- 8u - 8)Determine dh/du
- Q Let h(w) = - 5w (w-7)Determine the derivative of h.h' (w) = _____________.Determine the interval(s) on which h is differentiable. Report the solution using interval notation. h is differentiable on
- Q Let f(z)=?(8-4z)Determine the derivative of f.f'(z) =Determine the interval(s) on which f is differentiable. Report the solution using interval notation.f is differentiable on
- Q Let f(x) = xh(x) and h have the following properties. h(5) = 1 h'(5) = 3Determine f'(5).f'(5) =
- Q Let g(v) = -(-6v^2)/ (v-3)Determine the value(s) of v, if any, for which g has a horizontal tangent line.A) g has a horizontal tangent line at v =B) g has...
- Q Let f(x)= (-2x-3x - 8)/9Determine df/dx
- Q Let L: R ? R be the linear operator given by the ruleL(x, y) = (5x+3y, -4x - 2y).Find an ordered basis B for R such that[L]? =[2 0] ...
- Q Use Matrices to find the equation of the quadratic polynomial that goes through the points (-2, 79) (0, 7) and (1,1).
- Q Given f(x)=x/(x+3) and g(x)=2/x , find (fog)(x). What is the domain of the composition?
- Q Find the rate of change of f(x)=x+5x-12 on the interval [0, a].
- Q A truck with 32-in.-diameter wheels is traveling at 50 mi/h.Find the angular speed of the wheels in rad/min, "hint convert miles to inches & hours to minutes:_______ rad/minHow many revolutions...
- Q Maya earns 41 dollars per week working part-time at a book store. She makes one dollar more for each book that she sells. The amount, A (in dollars), that Maya...
- Q 1. Calculate y'. y =?x.cos?x2.. If f(x)=4cosx+sinx, find f'(x) and "(x).
- Q Determine how many x-intercepts the function y = 3 cos x + 5 has from 0 to 360.A) 0B) 2C) 4D) 6
- Q Find all the complex square roots of w =144 (cos 30 + i sin 30). Write the roots in polar form with ? in degrees.z? = __(cos__ + i sin__)(Type...
- Q Solve for all values of x.343^(2x+16) = (1/7)^(-2x+4x)
- Q The gas law for an ideal gas at absolute temperature T (in kelvins), pressure P (in atmospheres), and volume V (in liters) is PV = nRT, where n is the...
- Q Solve using Cramer's Rule.x +y +z = 11X-y +z = 32x + z = 12What is the solution of the system?
- Q Find the first derivative of the function f(?) = sin((e^2?)/(1+e^2?)). Then evaluate the first derivative when ?=?/2
- Q 9. Find the derivative of the function f(x)=sin(x + 1)10. Suppose that F(x)=f(g(x)) and g(14)=2, g'(14)=5, f'(14)=15, and f'(2)=12. Find F'(14).
- Q Solve using Cramer's rule.12x + 27y= -624x 9y = 9The solution is(Simplify your answer. Type an ordered pair, using integers or fractions.)
- Q A ray of light passes from air (n=1.00] into water (n=1.33) at an angle of incidence of 50. What is the angle of refraction?
- Q You are on a boat in the middle of the Pacific Ocean at the equator traveling in a hydrofoil going at a constant speed of 300 m/s. The water is...
- Q Use logarithmic differentiation to find the derivative of the function.y = (3x+1)(x?-6) Use logarithmic differentiation to find the derivative of the function y = x?^x
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