The organisms that make their own food are called ____.

Combine the following summations into one summation. +

 Organisms that spend their entire life cycle as plankton are called ____.

Given the following recurrence relationships:c1 + 2c2 = 02c2 + 6c3 = 0cn+2 = Find the general solution y = c0y1 + c1y2

 The ____ domain have evolved diverse metabolic abilities—some are photosynthetic, others heterotrophic—and are familiar to us as decomposers and disease agents.

Find all the first order partial derivatives for the following function.f(x, y) = (8x5y2 + 4)2

Determine if the given differential equation is exact. =

Use the improved Euler’s method with the specified step size to estimate the value of the solution at the given point x*. y’ = 3x + y, y(0) = 7, h = 0.2, x* = 1

Given the recurrence relationship: (n + 2)(n + 1)an+2 – an = 0 for n = 0, 1, 2, … find a6 and a7 in terms of a0 and a1.

Find the particular solution to the given differential equation that satisfies the given conditions.y”+ 4y’ – 21y = 0; y’ = 0 and y = 1 when x = 0