5. Find the absolute maximum and minimum values of the function -x² + 4x + 1 f(x) on the interval [0,4]. x+1 =

Q: Use implicit differentiation to find an equation of the tangent line to the curve at the given…

A:

Q: Is it possible to answer this using factoring, conjugate or any alternative methods? If so, could…

A: To evaluate the following limit. limx→0 x+13-1x

Q: Find the gradient of the function at the given point. Function Point f(x, y) (4, 5) Vf(4, 5) = x +…

A: Given function:- fx,y=x+5yy+1

Q: Find the limit. lim (3x)² = (Type +0<x (Type an exact answer.)

A:

Q: How many inflection points does ff have? Which points are inflection points? (List the labels of…

A: We have to find How many inflection points does function have.

Q: 16. Evaluate the limit for the graph: lim f(x). a. b. 3 | w 14 -1 4 -2 -2 0 +2 4 2 4 _0<x C. 0 els…

A:

Q: Find f'(x) and simplify. f(x) = 5x4 Inx

A:

Q: Find the distance from the point (-4,-6,4) to the line a(t) = ( – 5, 1, − 3)t + (− 7, — 4, 7) FORCYY

A:

Q: Use the method of cylindrical shells to find the volume of the solid obtained by rotating the region…

A:

Q: lim X-70 3√√x+1-1 X

A:

Q: The equation A(t) = 2000e0.045t gives the balance after t years of an initial investment of 2000…

A: Equation given A(t) = 2000e0.045t Find - (1)  dA/dt(2) Find and intepret A'(5)(3)  compare the…

Q: Find a set of parametric equations for the tangent line to the curve z = x² + y², z = 36 -y, (6, -1,…

A:

Q: Solve the given differential equation. 7ydx - 7xdy + x4 dx = 3dx The solution is. (Type an…

A:

Q: 1 I 1 1 1 1 I I 1 I 1 1 1 1 I 1 1 1 I 1 1 1 1 1 1 1 1 1 1 1 1 1 1 I 1 1 1 1 1 1 1 1 1 1 1 1 1 I I I…

A:

Q: Mr. Brust is running down his street. His position is given by the function p(t), where t is…

A: Mr. Brust is running down his street. His position is given by the function pt,  where t is measured…

Q: Differentiate y' = with respect to t. y = d cos(t) + t² sin(t)

A:

Q: Find the acute angle (in degrees) between the planes 3x Question Help: Pl Video 3y + z = 2 and 5x 4z…

A:

Q: Find the derivative of y = x² cot-¹(3x).

A:

Q: Water, at the rate of 12 cubic feet per minute, is pouring into a leaky container whose shape is a…

A:

Q: As the wheel of radius r cm in the figure rotates, the rod of length L attached to point P drives a…

A:

Q: f"(0) = sin 0 + cos 0, f(0) = 1, f'(0) = 4 f(0) = -sin (0) - cos(0) + (0) + 2 x

A: Given query is to find indicated function.

Q: x 18x² +81 Factor the denominator: - dx x²

A: Oo

Q: Use spherical coordinates to evaluate the triple integral  (e-((x^2)+(y^2)+(z^2)))/sqrt(x2+y2+z2)…

A:

Q: Classify and solve the following ODE. Make sure to submit a clear, complete, and detailed solution.…

A:

Q: The trough in the figure is to be made to the dimensions shown. Only the angle can be varied. What…

A: Figure :

Q: 5. Consider the region R bounded by y=1-x² x = 0 and y = 0 [This region is used to answer questions…

A:

Q: 10) Consider the following two functions p(t) = and 7e-2)-7 t-2 P: R R if 0 2 q: R→R q(t) =…

A:

Q: Compute the following limit: lim x→∞ e3x

A: Use the Taylor’s series extension of e3x and then simplify.

Q: Express these decimals in short form using the bar to designate the repeating part. Find the…

A: We can solve this as follows:

Q: Find the angle of inclination of the tangent plane to the surface at the given point. (Round your…

A:

Q: they​ occur, for the function f(x)=x2−18lnxon the domain [1,11].   Select the correct choice below​…

A:

Q: You are standing above the point (2, 2) on the surface z = 15 - (3x² + 2y²). (a) In which direction…

A: Please see the below picture for detailed solution.

Q: Can i still answer this without using the l'hospital rule? If yes, can you show me the alternative…

A:

Q: Consider the following graph of the second derivative, f" (x), for some function f (x): f"(x) 9- 6-…

A:

Q: Newton's Law of Cooling The temperature of a cup of coffee t min after it is poured is given by the…

A:

Q: find the volume of the solid revolution generated by revolving the region bounded by y=e^(3x) y=3…

A: Please see the below picture for detailed solution.

Q: Solve the differential equation by variation of parameters. y" - 2y' + y = et arctan(t) y(t): =

A:

Q: Find a plane containing the point (1,4,3) and the line of of the planes 7x + 5y - 8z = 27 and 5x +…

A:

Q: Use implicit differentiation to find an equation of the tangent line to the curve at the given…

A: By using implicit differentiation to find an equation of the tangent line  to the curve at the given…

Q: Calculate the double integral. ₂ yexy dA, R R= [0, 2] × [0, 5]

A:

Q: Find the triple integral of the function f(x,y,z) = x2cos(y+z) over the cube 3<x<4,0<y<pi,0<z<pi.

A:

Q: The position function of a particle is given by r(t) = (4t², (4t², 5t, t²- 1t). 1 At what time is…

A: rt=4t2, 5t, t2-1t To find the velocity, differentiate the position function with respect to t, we…

Q: Find a plane containing the point (-7,7,1) and the line of intersection of the planes - 3x - 3y + 6z…

A:

Q: Given Cost and Revenue functions C(q)=q3−11q2+55q+5000 and R(q)=−3q2+2400q​, what is the marginal…

A:

Q: Consider the following graph of f(x) 101 6- 4- V 2- 3 5 6 7 8 19 10 11 X -2- 8- -4- -6- -m A -L -00…

A:

Q: Question: is there a logarithmic property thay says: ln ∣ a - b ∣ is equal to - ln ∣ a + b ∣   Im…

A: Two concepts Trigonometry equations Logrithmic rule

Q: Change the Cartesian integral into an equivalent polar integral. Then evaluate the polar integral. 7…

A: As we know that x = rcosθy = rsinθ

Q: PTT/5 sin¹ (5x) dx =

A:

Q: Compute the product. This exercise should be done two ways: by hand and by using technology where…

A:

Q: Translate the given matrix equations into a system of linear equations. (Enter your answers as a…

A: Given, 01911-500xyzw = -25