Chain rule

You are given the function w=yz/x, where x=θ^2, y=r+θ and z=r-θ. Find ∂w/∂θ. a) using the appropriate chain rule b) converting w to a function of r,θ before differentiating. Which of the above is quicker?

Analysis/total differentials

Evaluate f(1,2) and f(1.05, 2.1) for the function ƒ(x,y)=x/y. a) calculate Δz b) use the total differential dz to approximate Δz

Sum of a series

Sum of a series

Functions,complex numbers

Questions on Functions,complex numbers

Indefinite integrals

Find the indefinite integrals (anti-derivatives):

Log differentiation

Find the derivative dy/dx if y = x^(x+3)

10 Calculus Problems

Please see attachments

Inequalities

Prove that if x>0, then 1+x/2-x^2/8<(1+x)^(1/2)<1+x/2

Taylor Approximation Related Problem

Please see the attached file for the fully formatted problems. Questions pertain to Second order Taylor approximations and integrals for two first order differential equations.

Two Segment Graph : Equation of Tangent and Calculation of Points

Please note: On the attached graph the scale is that each line represents one unit. Please show all work, thanks!! The graph of F consists of a semicircle and two line segments as shown (please see the attachment). Let g be the function given by: g(x)= def.integral from 0 to x f(t)dt. a Find g(3). b Find all value ...continues