Find the exact value of the area between the graphs of y = sinh x, y = cosh x, for −7 ≤ x ≤ 7.

Find the exact value of the area between the graphs of y = sinh x, y = cosh x, for −7 ≤ x ≤ 7.

If f(x) is even and ∫(from -2 to 2) (f(x) − 8) dx = 2, find ∫(from 0 to 2) f(x) dx

The average value of y = v(x) equals 2 for 1 ≤ x ≤ 5, and equals 11 for 5 ≤ x ≤ 14. What is the average value of v(x) for 1 ≤ x ≤ 14?

Find the exact average value of the function over the given interval. f(x) = 8x + 12 over [1, 7] average value=

So I struggle with optimization and we were given a problem and I have no idea on how to do it and I could really use some help please. So a person wants to ship a lot of packing peanuts but they...

Use linear approximation and calculate the error for f(x)=sinx , a=0 , Δx=0.5

What are the dimensions of the biggest possible volume (absolute maximum) of a triangular prism given the length and girth must equal 108 inches? Thanks! I struggle with optimization to...

Ross-Simons Company has a monthly advertising budget of $80000. Their marketing department estimates that if they spend x dollars on newspaper advertising and y dollars on television advertising,...

According to the data from a company, the marginal revenue of a product (in billions of dollars per year) is approximated by 3.91+0.07x+0.018x^2, where x=0 corresponding to 1986. What is the...

Hi, I just need to know if my explanation is ok. I think the question might be on my test tomorow. It asks to prove that f(x)= x^3+3x^2+6x has one real root. My explanation: f(1)=10>0 f(-1)=...

y= 4x-x^2-3lnx f'(x)= 4-2x-(3/x) My book is saying that its always decreasing, but when i look at the behavior before 0 , its negative and then after 0 its...

(a) f(x) = x2 - 2x from x = -1 and x = 2 (b) f(x) = 1/x - 1/e from x = 1 and x = e2

The manager of a plant has been instructed to hire and train additional employees to manufacture a new product. She must hire a sufficient number of new employees so that within 30 days they will...

The radius of the crowd increases at a rate of 6 ft/sec. How fast is the area taken up by the crowd increasing when the radius is 14 ft? Related Rates of AP Calculus!!!! Please help!...

a rectangular closed box of height h with a square base of side b has a volume V = 64m3 . the two squares bottom and the top side are made of material cost $20/m2 and the remaining sides cost $10/m2...

An ice cube that is 15 inches on each side is melting at the rate of 1.5in3 per minute. How fast is the length of its side decreasing

lim as x tends to 0+ (x^1/2)(lnx)

The radius of the pool increases at a rate of 5 cm/min. How fast is the area of the pool increasing when the radius is 5 cm? Related Rates of AP Calculus!!!! Please help!!!

The radius of the spill increases at a rate of 8 m/min. How fast is the area of the spill increasing when the radius is 8 m? Related Rates of AP Calculus!!!!Please help!!!!!

Hi, Im having trouble proving this. I only got half way through proving it. Its the Rolles Theorem part Im having trouble with. So first thing I did was show that there is a root by the IVT. f(0)=...

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