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1. For a function f : Z → Z, let R be the relation on Z given by xRy iff f(x) = f(y). (a) Prove that R is an equivalence relation on Z. (b) If for every x ? Z, the equivalenc
Exponential Functions : We'll begin by looking at the exponential function, f ( x ) = a x We desire to differe
Implicit Differentiation : To this instance we've done quite a few derivatives, however they have all been derivatives of function of the form y = f ( x ) . Unluckily not all
Find the center and radius of the circle whose equation is 3 x^2 - 8 x+ 3 y^2+ 4 y+ 2 = 0
Some interpretations of the derivative Example Is f ( x ) = 2 x 3 + 300 +4 increasing, decreasing or not changing at x = -2 ? Solution: We already know that the rate
Linda bought 35 yards of fencing at $4.88 a yard. How much did she spend? To multiply decimals, multiply generally, count the number of decimal places in the problem, then us
A poll tilts towards the sun at an 8 o angle from the vertical at it casta 22-ft shadow. The angle of elevation from the shadow to the top of the pole is 43 o . How tall is th
Higher-Order Derivatives It can be seen that the derivative of a function is also a function. Considering f'x as a function of x, we can take the derivative
Solve the linear equation: The equation relating the pressure that is denoted by P, to the force, F & the area, A, over which the force is applied is P =F/A. Solve this equat
Let u = sin(x). Then du = cos(x) dx. So you can now antidifferentiate e^u du. This is e^u + C = e^sin(x) + C. Then substitute your range 0 to pi. e^sin (pi)-e^sin(0) =0-0 =0
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