Give an example of: 1. An interval where the Mean Value Theorem does not apply when f(x)=1/x. 2. A continuous function f on the interval [−1, 1] that does not satisfy the conclusion of the Mean Value Theorem.

Q: Find f′(x) and f′(c).

A: Given fx=x2-4x-3  ;   c=1  

Q: #26. See

A: This question is related to series and sequence.

Q: Let θ be the angle between the line y = mx +b and the x-axis. Prove that         m = tan θ.

A: The slope of a line is the rate of change of the y-axis with respect to x. Formula for slope=riserun...

Q: Find all differentiable functions f: R→R such that f'(x) = F(x + n) – f(x) n for all real numbers x ...

A: As f'(x)=f(x+n)-f(x)n is true for all positive integers values of n thus substitute 1 for n in f'(x)...

Q: FR:  See

A:

Q: a) at what point does a local maximum occur?b) what is/are the value(s) of the local maximum

A:

Q: Evaluate: cos [sin cos[tan' +4 sin sec (" )

A:

Q: A particle travels along the path c(t) = (t3 – 6t2 – 15t, t? – 10t). Find the value t > 0 where the ...

A: Differentiate wrt t and then take magnitude for speed and put zero

Q: Find a positive angle and a negative angle that are coterminal with the given angle. 3 Enter an answ...

A: Adding 2π to original angle yields positive coterminal angle  Subtracting 2π to original angle yield...

Q: The function A(x) = 0.003x -0.04x +0.16x+0.02 approximates the blood alcohol concentration in a pers...

A: Given: Function A(x)=0.003x3-0.04x2+0.16x+0.02 To find where A(x) increasing and A(x) decreasing On ...

Q: termine wheter the geometric series is convergent or divergent. If it is convergent, find its sum. (...

A:

Q: At 1:00 p.m.., oil begins leaking from a tank at a rate of (4 + 0.75t) gallons per hour. , answer th...

A: At 1:00 p.m.., oil begins leaking from a tank at a rate of (4 + 0.75t) gallons per hour. , Let time ...

Q: Find an alternative form in terms of x for each of cos(sin-1 x) and tan(sin- 1 x).

A: In this kind of questions first remove the inverse trigonometric function by assuming them any varia...

Q: a. A bar lies along the +x axis, with one end at the origin. The bar's mass per unit length is given...

A:

Q: Find the surface area of y=6sin(6x) [0,pi/6] I can set up the integral and find the value with a cal...

A: Find the surface area of revolution 

Q: Find the sum of the series, if it converges. Otherwise, enter DNE. 20 Σ (-3)" 72 n=1

A:

Q: Which of the following series converge? |sin n| n2 n=1 n=1 n + 2 II. n2 + n n=1 A I only В Il only I...

A:

Q: Need help with C A is already answered, I got 21m^2. B is already answered, I got 28 - y

A:

Q: The speed of a runner increased steadily during the first three seconds of a race. Her speed at half...

A: A function is usually represented as f(x) where x is the input to the function and f(x) represents t...

Q: In thge given question, find the particular solution of the differential equation that satisfies the...

A: Given: dydx = 14+x2, y(2) = π To find: The particular solution  of the differential equation that sa...

Q: Evaluate without using a calculator. cot-1 1

A: Inverse function for a function is defined if and only if the function is one-to-one. The trigonomet...

Q: use trigonometric substitution:

A:

Q: If a function f has a Maclaurin series, what are the possibilities for the interval of convergence f...

A: Given: If a function f has a Maclaurin series, what are the possibilities for the interval of conver...

Q: Determine whether the sequence is convergent or divergent. Find the limit of the sequence if it is c...

A:

Q: Use the position function s(t) = −16t 2 + v0 t + s0 for free-falling objects.

A: The position function is given. Using this the velocity function is determined by taking its first d...

Q: Use the given function f to: (a) Find the domain of f. (b) Graph f. (c) From the graph,determine the...

A: Solution:Givenf(x)=3ex+2

Q: Apply the Mean Value Theorem for the functions over the given interval. 1. f(x) = 2x3 + 5x +1 over t...

A:

Q: The functions: y=x^2+(c/x^2) are all solutions of the equation xy'+2y=4x^2, (x>0). find the const...

A: note : The functions: y=x^2+(c/x^2) are NOT all solutions of the equation xy'+2y=4x^2, (x>0).   T...

Q: Determine if the graph is symmetric about the x-axis, the y-axis, or the origin. r = 9 sin 7θ

A: r=9 sin7θ Replace r, θ  by  r, -θ, we get ⇒r=9 sin7-θ⇒r=9 sin-7θ⇒r=-9 sin7θ Which is not same as ori...

Q: Find the solutions of sin(6x) + sin(2x)=0 for x in [0,2pi)

A: Givensin(6x) + sin(2x)=0 We need to find the solution for x in [0,2pi)

Q: #43. See

A:

Q: Find the local and absolute extremum for the functions over their domain: 3. f(x) = x*(x - 2)7

A:

Q: Q5 A, B, and C

A: Since you have asked multiple questions in single request so we will be answering only first questio...

Q: A car comes to a stop six seconds after the driver applies the brakes. While the brakes are on, the ...

A: The solution for the above question is as shown below.

Q: Find the following limits: a) lim (1 + 3x) lim[x- In(x+1)] b) sin 2x lim x0+ 5x d)- lim sec hx e) li...

A:

Q: A surveyor stands on a grassland and sees an evergreen tree on the side of a hill. Using their tools...

A:

Q: Find a power series, centered at 2, for the function f(x)% = 1 and the interval 5x - 2 on which the ...

A: Answer 

Q: 6. Let fbe the function defined by f(x) æ²+9 00 (a) Evaluate the improper integral | f(x) dx, or sho...

A: Answer 

Q: Use the given function f to: (a) Find the domain of f. (b) Graph f. (c) From the graph,determine the...

A: Since you have posted multiple subparts, as per our policy we will answer first three subparts. Plea...

Q: # 33, 39, 43 please

A:

Q: Alice, Bob, and Catherine stand at different points around the edge of a lake. The distance between ...

A: Given  Distance between Alice and Bob = 158yd  Distance between Bob and Catherine  = 106yd  Angle fo...

Q: #2   see attached image for question

A: Limit of a sequence

Q: 6 Find the r-coordinates of the inflection points for the polynomial p(z) + 20 I*+r+ 2021. 30 %3D

A: We have to find the point of inflection

Q: tind the domain and range y: sech X of find the derivahive of Ln (ten" x)

A: Domain  set of all input values where f(x) defined Range  set of all output values

Q: c hange each exponential statement to an equivalent statement involving an exponent. ln 4 = x

A: Given: Log 4=x

Q: Solve each equation. 4ex+1 = 5

A: Given 4ex+1=5

Q: (4 points) Let P = f(t) = 900(1.037)' be the population of a community in year t. (a) Evaluate f (0)...

A: You will find the respective values using the given equation that gives us the population of a commu...

Q: Determine whether the sequence is convergent or divergent. Find the limit of the sequence if it is c...

A: Given sequence

Q: Solve each equation. 8*102x-7 = 3

A:

Q: Find a power series, centered at 2, for the function f(x) = 1 and the interval Зд — 2 on which the e...

A: according to the given problem, we have

Limits

When it comes to calculus, limits are considered to be a very important topic of discussion. The main importance of limit lies in expressing the value of a function as it gets closer to a certain value. Also, limits can help you to understand other topics, such as continuity and differentiability better. In a broader sense, every calculus notion is a limit. Other branches of calculus have also been derived from limits.