Consider the function f(x) interval. = 1 on the interval [3, 9]. Find the average or mean slope of the function on this X By the Mean Value Theorem, we know there exists a c in the open interval (3, 9) such that f'(c) is equal to this mean slope. For this problem, there is only one c that works. Find it, and enter the exact value.

Q: The function f has a continuous second derivative, and it satisfies ƒ(−4) = −5, ƒ'(−4) = 3 and…

A: The solution is shown below-

Q: From the graphs of f and g in the figure, we find the following. (Assume that each point lies on the…

A:

Q: cos x ln(sin x)dx

A:

Q: A farmer finds that if she plants 40 trees per acre, each tree will yield 20 bushels of fruit. She…

A: According to the given instruction, the answer is as follows

Q: Consider the function f(0) = 7sin²0 - 7cos0. a) Find f'(0) = 7 sin (20) + 7 sin (0) (b) Find the…

A: Consider the function f(θ)= 7sin2θ-7cosθ.  a) Find f' b) Find the critical points on the interval…

Q: (a) Find the linear approximation L(x) of 2 f(x) = x³ at x = 3 L(x) = x = 27. (b) Use L(x) to…

A: The given function fx=x23. To find the linear approximation of fx at x=27.

Q: Evaluate the Limits: a) limt->-1(t2+3t+2)/(t2-t-2) b) limx->9 (9x-x2)/(3-x1/2) c) limx->-inf…

A:

Q: A 200-foot cable weighing 5 pounds per foot is hanging from a winch 200 feet above ground level.…

A:

Q: The number of cell structures in a Minbari stem cell (fictional) is modeled by f(t) = 1 + 30t - 10t³…

A:

Q: Consider the following series. Answer the following questions. Σ (x + 7) n 2n n=0 1. Find the values…

A:

Q: 26. Distinguish between average and instantaneous rate of change, use an answer. appropriate example…

A:

Q: Find the general solution of the following reducible second-order differential equation. Assume x, y…

A: Note :- Since you have posted multiple questions, we will provide the solution only to the first…

Q: Solve the equation y" +4y= S(t-4π), y(0) = 1/2, y'(0)=0

A: The given differential equation: y''+4y=δt-4π, y0=12, y'0=0

Q: 1 3 I(t) = ²/³ - 5 ² + 3 2 +86 (0 ≤ t ≤ 10)

A: I(t)=13t3-52t2+86for critical numbers put I'(t)=0d dt(tn)=ntn-1d dt(constant)=0

Q: Use linear approximation, i.e. the tangent line, to approximate 4.7² as follows: Let f(x) = x². The…

A: f(x)=x2m=f'(x)d dx(xn)=nxn-1

Q: A ball bearing is placed on an inclined plane and begins to roll. The angle of elevation of the…

A: Given: The angle of elevation of the plane is θ= pi/9 The distance (in meters) the ball bearing…

Q: 3x³+1 f) lim x →∞0 4x³-1

A:

Q: Find an equation of the tangent line to the graph of the given function at the specified point. x²-1…

A:

Q: Solve the equation for x given that 1 ≤ x ≤ 8: ln x = sin x, using 5 iterations of Newton's method.

A: To find the solution of the following equation ln x = sinx by using Newton's method For the…

Q: 6. Evaluate the limit: lim x+-5+ a. 25 b. 2.5 5x X+ 5* C. c. -25 -co d.

A:

Q: Find the interval(s) where the function is increasing and the interval(s) where it is decreasing.…

A: A function y=f(x) is said to be increasing in the interval (a,b) if for every x∈(a,b), f'(x)>0.…

Q: Solve using the elimination method. 0.2x 0.5y = 1.1 0.5x 0.2y = 1.7 (Hint: Since each coefficient…

A: 0.2x-0.5y=-1.1.....(1)0.5x-0.2y=-1.7..........(2)

Q: Find the maximum of f(x, y, z) = x + y + z subject to the two constraints x² + y² + 2² = 6 and 1x² +…

A: Solution below

Q: that the cords have been disconnected from the device. "Computer, how do I plug in these cables",…

A: f(x)=ln(3x) f'(x)=313x = 1x f'(c)=1c   it is required Red cord.

Q: Identify the open intervals on which the function y=9x-18 cosx, 0<x<2pi is increasing or decreasing.

A: A function y=f(x) is said to be increasing in an interval a,b if for everyx∈ a,b, dydx=f'(x)&gt;0.…

Q: Consider the following. Sk (4x - y) da, where R is the region in the first quadrant enclosed by the…

A: Given that  R is the region in the first quadrant enclosed by the circle x2+y2=4and the lines x=0…

Q: The average rate of change of f(x) = X a. 2 b. 0.5 over the interval 1 ≤ x ≤ 2 is c. -0.5 d. -1

A: we will find the required.

Q: For a certain mammal, researchers have determined that the mesiodistal crown length of deciduous…

A: Given: Crown length (in mm) of the molar t weeks after conception L(t)=-.015t2+1.38t-7.1 To find:…

Q: 1. Find the length of the arc of the curve 3 (2 x − 1)² from x = 0 to x = 8 - y = 32/2 (2x

A: Given :y=2322x-132

Q: let y = 5 log2 x³ find y' O 15/(In2 +x) O 15/x O (5/In2)(3/x) noe of the above

A:

Q: Use the graphs of f and g shown below to find the following: (a) g (f (2)) = (b) f (g (4)) EHH f(x)…

A:

Q: c) lim x³+1 X-2x+1

A:

Q: . Evaluate the limit for the graph: lim f(x). |y4 4 a. 3 b. 2 2 -4-20 2 -2 -++-% x c. d. 5 does not…

A: We will find the required.

Q: Consider the ellipse 4x² + 2xy + 2y² = 88. (a) The derivative on this curve is dr dy = dx (b) Find…

A:

Q: Let f(x) = 7x sin(x) cos(x). Evaluate 3TT f'(x) at x = 3³77₁ ƒ' (³)

A: f(x)=7xsinxcosxd dx(sinx)=cosxd dx(cosx)=-sinxd dx(a.b)=adbdx+bdadx

Q: 1. Make a sketch for each parabola a. y² = 4x b. x² =−16y

A: To draw parabolas

Q: 3. Find the slope of the tangent line of the following curves at 0= 1/3 r = 2 cos Ⓒ

A: We can solve this as follows:

Q: The graph of y = f(x) has ƒ(5) = -2, f'(5) = 2, and f'(5): = -1. Which of the = −1 following might…

A:

Q: Determine whether the sequence is divergent or convergent. If it is convergent, evaluate its limit.…

A: On finding the limit of the given sequence we will check the given sequence is convergent or…

Q: If n(A) = 28, n(B) = 25, n(C) = 24, n(A n B) = 8, n(An C) = 12, n(B n C) = 7, and n(A U BUC) = 55,…

A: To find n(AΠBΠC)

Q: Calculate the derivative of the function. HINT [See Example 3.] h(x) = 3[(6x − 1)(x − 1)]−1/3

A:

Q: The graph of y=f(x) has f(5) = 1, f(x) has f(5) = 1, f'(5) = -1, and f(5) = -1-

A:

Q: Find an equation of the plane with the given characteristics. The plane passes through (0, 0, 0),…

A:

Q: Two circles have the same center. The inner circle has radius r which is increasing at a rate of 3…

A:

Q: Find the point on the graph of the function f(x)=(sqrt x) that is closest to the point (18,0) .…

A: The solution is shown below-

Q: Find the limit lim x (tan x) cos(x)

A: L'Hospitals Rule:

Q: Sketch the region whose area is given by the integral. Evaluate the integral. 8 sin(0) £726² π/2 J r…

A: .

Q: Find the rate of change of total revenue, cost, and profit with respect to time. Assume that R(x)…

A:

Q: (b) g(x) = (x + e*)², [0, In 4]

A:

Q: do you know the formula for finding integrals

A: