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1.Verify that the hypotheses of the Mean-Value Theorem are satisfied for the function ?(?) = (√(? − 1) + 1) on the interval [2,10], and find all values of ? in the given interval that satisfy the conclusion of the theorem.

2. Verify that the hypotheses of the Rolle’s Theorem are satisfied for the function ?(?) = (?^2−1)/(?−2) on the interval [−1,1], and find the value of ? in the given interval that satisfy the conclusion of the theorem.

3. Evaluate lim ?→ ∞ (√(4?+1)+√(4?−1) / (?) ) . Hint if divide by x or x^2 then please show to understand.

4. State the ...

a. Mean-Value Theorem

b. Rolle's Theorem

A survey of 500 high school students was taken to determine their favorite chocolate candy. Of the 500 students surveyed, 159 like Snickers, 151 like Twix, 176 like Reese's Peanut Butter Cups, 90 like Snickers and Twix, 99 like Twix and Reese's Peanut Butter Cups, 108 like Snickers and Reese's Peanut Butter Cups, and 56 like all three kinds of chocolate candy. How many students like no more than one kind of these chocolate candies?

a) 255

b) 315

c) 189

d) 60

e) 185

f) None of the above.

1b.

A survey of 500 high school students was taken to determine their favorite chocolate candy. Of the 500 students surveyed, 129 like Snickers, 118 like Twix, 145 like Reese's Peanut Butter Cups, 22 like Snickers and Twix, 54 like Twix and Reese's Peanut Butter Cups, 55 like Snickers and Reese's Peanut Butter Cups, and 8 like all three kinds of chocolate candy. How many students like Snickers, but not Twix or Reese's Peanut Butter Cups?

a) 129

b) 69

c) 61

d) 60

e) 121

f) None of the above.

set up the mclaurin series for f(x) = e^x....afterwards find the terms needed to approx. f(2pi) for an error less than 10^-7... I'm not sure what to do with that f(2pi)

1. Si U=(x²+y²+z²)^-1/2 , demuestre que ∂²U/∂x²+∂²U/∂y²+∂²U/∂z²=0

The displacement (in meters) of a particle moving in a straight line is given by s = t^2 - 4t + 16, where t is measured in seconds.
(a) Find the average velocity over each time interval.
(i) [3, 4]


(ii) [3.5, 4]


(iii) [4, 5]


(iv) [4, 4.5]

(2 or 3 sentences are fine) tell me a little bit about calculus- whats it all about ?

Find the 4th roots of i. Sketch them in an Argand diagram.

Use the first and second derivatives of f(x)=3x⁴+4x³-96x²-192x+284 to give as much information about the graph of the function as possible. Use this information to sketch the graph.

1.) Convert the following from rectangular coordinates to cylindrical coordinates. Write your angles in degrees rounded to one decimal point
(3, -7, 4)

2.) Convert the following from rectangular coordinates to spherical coordinates. Write your angles in degrees rounded to one decimal point
(3, -7, 4)

3.) Convert the following from cylindrical to rectangular coordinates. Round your answer to one decimal place.
(3, 20^o, -4)

4.) Convert the following from sphereical to rectangular coordinates. Round your answer to one decimal place.
(3, 20^o, -40^o)

1. What is a critical number of a function f ? What is the connection between critical numbers and relative extreme values?

2. What are inflection points? How do you find them?

3. What does the sign of the derivative, f ', tell us about the function? What does the sign of the 2nd derivative, f ", tell us about the function?

4. What does it mean to say that a function is concave upward? Concave downward?

5. What does the Extreme Value Theorem say? Explain how to find the absolute extrema of a continuous function on a closed interval.

6. Explain how to use the 2^nd derivative to find the relative maxima and relative minima of a function.

7. What is the meaning of Δy/Δx? What is its geometric interpretation? What is the meaning of dy/dx? What is its geometric interpretation?

8. For which functions is dy/dx equal to Δy/Δx?

9. When is dy about equal to Δy?

10. What is marginal cost? If C(x) is a cost function, how would we find the marginal cost when x = 50? What does it represent?

What it means the degree of g(x) is 0?
(g(x) is a non zero element of N of minimal degree. Where N is an ideal in F[x]. )
the geometrical meaning of degree of polynomial is 0?

how are the knowledge of lines shapes and forms useful in art appreciation and creation?

In 1950, Brian's dad recieved $20 for his tenth birthday. His mother deposited it into a bank account for him. Everyone forgot about the money and made no further deposits or withdrawls. The table shows the account balance for several years.

5A) Enter the info on your calculator. Look at the scatterplot. What type of function represents this curve?

5B)what is the equation of best fit? Round all values to the nearest hundreth

5C)Use your equation to estimate the balance in the account when Brian's dad turn 70

Please show work will rate if done all questions