The Differentials: Example 7

Problem:Find $latex d\left[ln{\left(y^2\right)}+ln{\left(1+\sqrt y\right)}\right]&s=3&bg=ffffff&fg=000000$. SOLUTION: $latex =d\left[ln{\left(y^2\left(1+\sqrt y\right)\right)}\right]&s=1&bg=ffffff&fg=000000$$latex =d\left[ln{\left(y^2+y^\frac{5}{2}\right)}\right]&s=1&bg=ffffff&fg=000000$$latex =\frac{1}{y^2+y^\frac{5}{2}}\times\left(2y+\frac{5}{2}y^\frac{3}{2}\right)dy&s=1&bg=ffffff&fg=000000$$latex =\frac{y\left(2+\frac{5}{2}y^\frac{1}{2}\right)}{y^2\left(1+\sqrt y\right)}dy&s=1&bg=ffffff&fg=000000$$latex =\frac{2+\frac{5}{2}y^\frac{1}{2}}{y\left(1+\sqrt y\right)}dy&s=1&bg=ffffff&fg=000000$$latex =\frac{2+\frac{5}{2}\sqrt y}{y\left(1+\sqrt y\right)}dy&s=1&bg=ffffff&fg=000000$ 

Openstax Calculus Volume I| Functions and Graphs| Review of Functions | Problem 1

For the following exercises, (a) determine the domain and the range of each relation, and (b) state whether the relation is a function.   x -3 -2 -1 0 1 2 3 y 9 4 1 0 1 4 9 SOLUTION: The domain is $latex \left\{-3,\:-2,\:-1,\:0,\:1,\:2,\:3\right\}&s=1&fg=000000$. The range is $latex \left\{0,\:1,\:4,\:9\right\}&s=1&fg=000000$. Since there is exactly one output for … Continue reading Openstax Calculus Volume I| Functions and Graphs| Review of Functions | Problem 1