Homework Statement
Find \frac{dy}{dx} if y = \sqrt{5u^2 -3} and u = \frac{2x}{3x+1}
Homework Equations
Chain Rule
\frac{dy}{dx} = \frac{dy}{du} x \frac{du}{dx}
The Attempt at a Solution
\frac{dy}{du} = 5u(5u^2 - 3)^-1/2
\frac{du}{dx} = -6x(3x+1)^-2
\frac{dy}{dx} =...
Yeah sorry, I edited the original questions (and know I know how to show the limit's now haha).
So then my answers for 10/x would be 0. the one with "a" as a variable would be 0. and then the one with the absolute would be 1?
Before we start, can you just explain how to start me off? I understand the idea of all limits, just a few tricky ones that were assigned for homework. (note: ALL limits are x --> infinity)
Homework Statement
lim ^{}\frac{10}{x}lim \frac{x^{2}+a^{2}}{x^{3}+a^{3}}lim (1 - r^{x}) , |r| < 1...
For which value of x...horizontal Tangent Line
Homework Statement
For which value of x does f(x) = \frac{k}{ax^{2}+bx+c} have a horizontal tangent line?
Homework Equations
Quotient Rule?
F'(x) = [g(x)a'(x) - a(x)g'(x)]/g(x)^2?
The Attempt at a Solution
Am I supposed to...
Homework Statement
Supposed "f" is a differentiable function. Write the expression for the derivative of the following function.
a) h(x) = -4x^3 * f(x)
b) h(x) = 2/\sqrt{x}* f(x)
Homework Equations
N/a
The Attempt at a Solution
Would the answers just be (using the product...
ah sorry, its actually supposed to be "/2", that way its half the area, sorry the drawing didnt show up. its supposed to be a semi-circle connected to a rectangle.
sorry, that was a typing error as well haha.
A = L * D + (pi*d)/2
which becomes
A = 8 - d/2 - ((pi * d)/4)
this still...