mathwiz

Given: 2.0 L solution of .5 M Hydrofluoric acid and .5 M sodium fluoride

Ka = 6.4 x 10^-4

If 0.010 moles of Hydrochloric Acid (solid) is added to the 2 liter buffered solution, what is the new pH?

My local vw dealership has a 2008 clearance going on right now. They have a demo (about 4000 miles...) 2008 Passat 3.6 4motion with navigation, premium wheels, dynaaudio, and a premium grille. They are offering this car for $29,995. Do you guys think this is a good deal, or not?

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I have attempted to solve this problem in many ways, but I just haven't come up with anything useful. I know it's got something to do with derivatives. Could I please get some help? The question is as follows:

Let (a,b) be an arbitrary point on the graph of y = 1/x, x > 0. Prove that the area of the triangle formed by the tangent line through (a,b) and the coordinate axes is 2.

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Using kinematic equations, solve the following problem:

Two racers are next to each other. One is traveling at a constant speed of 27 m/s. The second car starts from rest and has a constant acceleration. What acceleration must the second car have if the cars are to meet up again in 1.8 km?

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I am confused on this question.

Let f be the function given by f(x) = 2 ln(x^2 - 5) - x with the domain of 3 less than or equal to x less than or equal to 6.

First, Find the x-coordinate of relative maximum point of f if exists. Justify this part using calculus.

Second, Find the absolute maximum value of f(x) on 3 less than or equal to x less than or equal to 6.

Finally, write an equation of the line tangent to the graph of f at x=4.

I know it looks a bit long, but once you start, you'll be on a roll.

Thanks!

Can someone please help me differentiate this equation?

xy^2 + 5 = 4x^3y

Please help me find dy/dx for y^2 + 2e^(-xy) = 6.

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I do not know how to figure out this problem. Please help.

What is the area of the largest rectangle that can be inscribed in the region bounded by y=3-x^2 and the x-axis?

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Here's the original question:

Let f be a function given by f(x) = 2e^(3x) and g be the function be given by g(x) = 8x^3. At what value do the graphs of f and g have parallel tangent lines?

I found that f '(x) = 6e^(3x) and that g '(x) = 24x^2. What do I do from here?

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I do not know how to do this problem. Please help.

The top of a 17-foot ladder is sliding down a vertical wall at a constant rate of 2 feet per minute. When the top of the ladder is 8 feet from the ground, what is the rate of change of the distance between the bottom of the ladder and the wall?

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Let f be a differentiable function such that f(3) = 2 and f '(3) = 10. If the tangent line to the graph of f at x = 3 is used to find an approximation to a zero of f, that approximation would be what?

OK, so I found the tangent line is y = 10x - 32. What do I do from here?

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Let f be a differentiable function such that f(3) = 2 and f '(3) = 10. If the tangent line to the graph of f at x = 3 is used to find an approximation to a zero of f, that approximation would be what?

OK, so I found the tangent line is y = 10x - 32. What do I do from here?

Thanks!

Here is the function: 2y^2 - 3x^2 = 18 - 2xy

The first piece is x+3 where x is less than or equal to 2.

The second piece is 6x-7 where x is greater than 2.

Figure out if lim(x-->2) f(x) exists.

Then figure out if f(x) is continuous at x=2.

And finally, figure out if f(x) is differentiable at x=2.

Thanks!!

lim(theta-->0) of (cos(theta) -1) / (2sin^2(theta))

The point A(4, 2) is translated by the vector v = <-7, -3> and then reflected in the x-axis. Find the coordinates of its image, A'.

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Do any of the below functions not have an inverse (ie. not one-to-one)?

f(x) = (x+1)^(1/3)

f(x) = x^3 + x + 1

f(x) = 3/(x^3) - x

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Here is the function:

f(x) = (x+1)^(1/3)

If f(x) has an inverse, calculate it.

Can someone please explain how to do this?

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Use implicit differentiation to find dy/dx of the following equation:

x - (1/2) = -cos(y)

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I've been stuck on this question. Can someone please help?

Find dy/dx for the following using implicit differentiation:

ln(xy) + y^2 = 1

Thanks!