5. a) Determine whether the Mean Value Theorem can be applied to f (x) = x²/3, [1,8] %3D b) If the MVT can be applied, find all values of c in the open interval (a, b) such that f'(c) = f(b)-f(a) (you can leave the answer as a fraction) If the MVT cannot be %3D b-a applied, enter NA.

Q: 1 dx x2 V25 – x2

A: since you have posted multiple question in this question which are not interlinked so i have solved…

Q: Integrate the following:  use the U-substitution. ∫ (x2+5x)dx/4√x+9

A: Given problem:- Integrate the following:    use the U-substitution.   ∫ (x2 +5x)dx/ 4√x+9

Q: 50) If f(x) = r° cos(x³), then f() (0) is d) 5! а) 0 b) 1 с) 3! e) f(5) (0) does not exist. 51) If…

A: f(x)=x3cos(x3)f(x)=x3∑n=0∞(-1)n(x3)2n(2n)! f(x)=x31-x62! +x123!+...f(x)=x3-x92!…

Q: A supermarket manager estimates that a total of 400 cases of soup will be sold at a steady rate…

A:

Q: Solve using an appropriate method on First Order Differential Equation. Show complete and detailed…

A:

Q: A curve C is defined by the parametric equations x = 1– t2 y = t – t3 (a) Show that C has two…

A: Since the student has posted many sub-parts of the question and does not mention any specific part,…

Q: Use Theorem 13.9 to find the directional derivative of the function at P in the direction of the…

A:

Q: —х-1 6. (LO 5) Let f (x) Find the absolute maximum and minimum values of f(x) x2+3 on the interval…

A: Solve the following

Q: 7/4 *(1 – sin 2t)3/2 cos 2t dt

A:

Q: (cos x+xcost)dt +(sint – t sin x)dx = 0 Ans. t cos x+x sint = c

A:

Q: Evaluate the indefinite integral, ſ cosh? x dx.

A:

Q: Find f'(1) for f(x) = In(v6x – 3).

A:

Q: Given the points A(-1, 2, 0), B(1, 0, 3) and C(1, 0, 2), find AB • AC x BC.

A:

Q: Determine if is a p-series or not. If so, determine if the series converges or 7 5ni n=1 diverges,…

A:

Q: Solve the initial value problem -4sin(2t – 4), s'(0) = 100, s(0) = 0. %3D %3D dr2

A:

Q: Find a function of the form y A sin(kr) + C or y = A cos(ka) + C whose graph matches the function…

A: Given query is to find function finthe graph.

Q: Use the shell method to write and evaluate the definite integral that represents the volume of the…

A: Given

Q: 8xy® 8x8 + 8ys if(x, y) ± (0,0) Let f(x, y) if (x, y) = (0,0) 3xy® За? + 3у12 if (x, y) + (0,0) and…

A:

Q: Use the integral test to determine whether the following is convergent or divergent. Vn(1+/n)

A: Solve the following

Q: The radical function f(x) is represented by the equation f(x) = x-1+4· The graph shown is the graph…

A: Given function fx=x-1+4 We know x-1 is defined for x-1≥0    ⇒   x≥1Therefore fx=x-1+4  is defined…

Q: An equation relating demand q and price p given. Compute the elasticity of demand for the given…

A: We will find the elasticity.

Q: What is the general solution to the differential equation x de = y + y cos x ?

A: Let's find.

Q: Write and evaluate the definite integral that represents the volume of the solid formed by revolving…

A:

Q: 3. The following curves bounds a certain area: y = 4x – x2 y = 4 and x = -2 Determine that area.

A:

Q: Suppose that o f(x) dx = 3. Find , f(x) dx if, %3D

A:

Q: Find the maxima and/or minima of f (x, y,z) = 2x2 + y2 + 3z2 subject to the constraint 2x - 3y - 4z…

A:

Q: Use a graphing calculator to help sketch each graph on the coordinate plane. Note: The general form…

A: Hello learner, we can answer the first question as per the honor policy. Please resubmit other…

Q: | e" sin® (e") cos" .7 (e²)dx

A:

Q: 12-2t+tcos(t)-tet-4t2 Given a velocity function v(t) with initial condition s(1) = e, find the…

A: Given query is to find the position function.

Q: pls show full solutions and clear   1. Show that the absolute value function is continuous at x =…

A:

Q: y, = x2 + 2x + 2 Y2 = 2x + 18 dx 25- 20 15 y 10- 5- 6.

A:

Q: (x + 1)³sinx dx x+1)° cosx+3 (x + 1)2 sin x-6 (x + 1)cosx-6 sinx+ C | (x + 1) cos x 3 (x + 1)2 sin x…

A: Solving the problem by finding the integral by oarts method.

Q: 2. Determine the equation of the line perpendicular to the tangent line to the function f(x) = e' at…

A: We will find the equation of the line.

Q: A hot air balloon sing vertically is tracked by an observer located 3 miles from the lift-off point.…

A: let the height at that moment is h miles.

Q: nt) Let I be the length of a diagonal of a rectangle Whose Sides Rave lengins If increases at a…

A:

Q: Using a graphing calculator, estimate the real zeros, the relative maxima and minima, and the range…

A: Please see the answer below.

Q: |*| +1, {0, x = 0 1x-1, x >0

A:

Q: For the function g(x) =x - 9x° solve the following. 3 g(x) <0 .... Select the correct choice below…

A: The given function is: gx=x5-9x3 Solve  gx&lt;0

Q: s) Let f(x) = 6x2 - 8x4 Find the open intervals on which f is increasing (decreasing). Then…

A: Given

Q: / Väde= 6.

A:

Q: Given f(x, y) = In(3x² + 5y²) then af dx

A:

Q: Solve this q3 as soon as possible and not use p. Take (p=6) and solve this plz with p=6

A: Follow the procedure given below.

Q: 10. * S sin(In x)dx 1 C x sin(Inx) – cos(Inx) + C 2. x sin(Inx) – cos(lnx) + C 1 x sin(lnx) +…

A:

Q: 3. Find the radius of convergence and interval of convergence of the series (3x + 2)" (a) n! n=1

A:

Q: finde general Sonotion 1- y' = See'y 2X-1 %3D 2- 3-Xy=Y+2x $ in?

A: This question can be solved by applying the concept of differential equation.

Q: Consider the function f(x) = 2x + 18x? – 42x + 9, - 7< x < 2. This function has an absolute minimum…

A:

Q: If g(2) = 3 and g'(2) = 1 and f(x) = [g(x)]°, find f'(2) %3D

A:

Q: Find all the local maximum and minimum and saddle points, with their values, for the function f(x,…

A:

Q: 4. Solve the matrix equation for x and y. 2 1 5 3 -2 -2 1 x 9 5 у %3D 1 -3

A:

Q: T sec"(evE + 1) dx Vxe-Vx

A: