Calc Help Offered

Lol, I have a test on vectors and a test in chem, so that's a problem that's just gonna have to wait. :p

okay, vectors are pretty tough, gl on your tests.

Hey, I could use some help with these problems.

1) Given the curve x+xy+2y^2=6

a) Find an expression for the slope of the curve at any point (x,y) on the curve.

b) Find an equation for the line tangent to the curve at the point (2,1).

c) Find the coordinates of all other points on this curve with slope equal to the slope at (2,1).

2) Given the curve x^2-xy+y^2=9.

a) Write a general expression for the slope of the curve.

b) Find the coordinates of the points on the curve where the tangents are vertical.

c) At the point (0,3) find the rate of change in the slope of the curve with respect to x.

3) Let f be the function defined as follows:

f(x) = {abs(x-1)+2, for x < 1}
{ax^2+bx, for x > 1, where a and b are constants}

a. If a = 2 and b = 3, is f continuous of all x? Justify your answer.
b. Describe all values of a and b for which f is a continuous function.
c. For what values of a and b if f both continuous and differentiable?

1) Let f be a real-valued function defined by f(x)=sqrt(1+6x).
a. Give the domain and range of f.
b. Determine the slope of the line tangent to the graph of f at x = 4.
c. Determine the y-intercept of the line tangent to the graph of f at x = 4.
d. Give the coordinates of the point on the graph of f where the tangent
line is parallel to y = x + 12.

2) Let f be a function defined by f(x)={2x+1, for x < 2,
{1/2x^2+k, for x > 2

a. For what values of k will f be continuous at x = 2? Justify your answer.
b. Using the value of k found in part (a), determine whether f is differentiable
at x = 2. Use the definition of the derivative to justify your answer.
c. Let k = 4. Determine whether f is differentiable at x = 2. Justify your
answer.

3) For all real numbers x and y, let f be a function such that f(x+y) = f(x) + f(y) + 2xy and such that the limit as (h) approaches 0 of the function f(h)/h=7.

a. Find f(0). Justify your answer.
b. Use the definition of the derivative to find f’(x).
c. Find f(x).

Oh man...I came here to ask questions and I ended up trying to follow the epic-might I also say quite nerdy :)- duel off between chessmaster and pianogirl. Never going to try that again.

Anyways, I'm doing applications of derivatives now. More specifically, I'm locating extrema by using derivatives and then I think I'm supposed to draw the graph. We're using Rolle's theorem and the MVT also. If you have any hints or useful tips that can help me, please mention them. As for the bulk of the understanding...I have a date with the textbook tonight.

I'm taking precalculus this year (lots of trig stuff), but this last marrking period we're learning the beginnings of calculus (we just did limits, and now we're starting derivatives). I'm pretty confused with the concepts of derivatives and tangent lines and slopes, so can someone clarify for me the diferrence between these things?

Can someone please help me, ive been stuck on this problem for a couple of hours.
btw sorry if its hard to read, idk how to fractions and limits on the computer.

Let f be the function that is given by
f(x)= (ax+b)/(x^2-c) and that has the following properties

i) the graph of f(x) is symmetric with respect to the y-axis
ii) the limit as x approaches 2 from the right of f(x) is positive infinity.
iii) f ' (1)= -2

Find a, b, and c

I already found that c=4, i just need help with finding a and b.
Thanksss(:

mahdees1;93900 wrote:Can someone please help me, ive been stuck on this problem for a couple of hours.
btw sorry if its hard to read, idk how to fractions and limits on the computer.

Let f be the function that is given by
f(x)= (ax+b)/(x^2-c) and that has the following properties

i) the graph of f(x) is symmetric with respect to the y-axis
ii) the limit as x approaches 2 from the right of f(x) is positive infinity.
iii) f ' (1)= -2

Find a, b, and c

I already found that c=4, i just need help with finding a and b.
Thanksss(:

Alright, so I worked on this a bit, and it frustrated me, and then I realized, the x totally throwing off the symmetry. If that x exists on the top, the function cannot be symmetric about the y-axis, so the a has to be 0.

From there you have b/(x^2-4). Just take the derivative at 1, set it equal to -2, and finding b will be simple.

Hi all, a lot of similar integration problems is solved at [URL=http://www.math24.net/list-integration.html]http://www.math24.net/list-i....

hmm, Perhaps you did substitute, but I see no dx, I see no integration. I see a trig equation and nothing more....