Line Equations : Tangents & Normals

i) Find the equation of the tangent to y=x(1-x) at x=1 ii) Find the equation of the normal to y=x(1-x) at x=1 iii) Find the equations of the tangents to y=x(1-x) that pass through (-1, 1/4)

Finding tangent through a certain point (involves drawing a diagram)

A portion of a river has the shape of the equation y=1-x^2/4, where distances are measured in tens of kilometres, and the positive y-axis represents due north. the town of Coopers Crossing is situated on the river at its most northerly point. The town of Black Stump is 10 kilometres due south of Coopers Crossing. the town of And ...continues

Implicit differentiation

If x^2+y^3=y+y^4, then find dy/dx

Radius of Convergence

Find the radius of convergence of the series in the attached file 'Series.doc'.

Discontinuous function

Define a discontinuous function and state the conditions for discontinuity. Find whether the following functions are discontinuous: f(x)=1/x and f(x)=(x)^(1/2) Solve the following:(involves jump discontinuity) A tomato wholesaler finds that the price of newly harvested tomatoes is $16 per pound if he purchases fewer th ...continues

Discontinuity of an oscillatory function

Let f(x)=sin(1/x) if x is not equal to 0 =0 if x is equal to 1 Check whether f is continuous at 0(zero)?

Intermediate value theorem: Definition, Illustration by Graph and its application

Define Intermediate-Value theorem Using this theorem, show that there is a root of P(x)=x^3+x^2+x-1 in the closed interval [0,1].

Example of a function continuous over (- infinity, + infinity)

Prove that f(x)=|x| (Absolute value of x) is continuous over the interval (- infinity, + infinity)

Convergence of Series

Determine whether the series Sum(n!/n^n) n=1..infinity is absolutely convergent, conditionally convergent or divergent.

Integration By Trigonometric Substitution: Solving Trickier Problems?

Hello! I'm having trouble using Trigonometric Substitution to find the anti-derivative of non-simple integrands. For details on my situation, please consult my missive, which I've included as an attachment in MS Word '95 (WordPad compatible) and Adobe PDF (ver 3+) files. (The files contain identical information; if you can re ...continues