Calculus Answers

Differentiate the following function: f(x)=ex+xe

The equation for a projectile's height versus time is n(t) = -1662 +V++ to
A tennis ball machine serves a ball vertically into the air from a height of 2
feet, with an initial speed of 120 feet per second. What is the maximum
height, in feet, the ball will attain?
Round to the nearest whole foot.

Let E(t) be the number of errors made by a resident from the start of a shift until t hours into the shift. The instantaneous rate of change of errors made is E′(t) = t3 − 3 t2 + 2. (i) Sketch E(t). Label any minima, maxima and/or inflection points. On the same axes, draw a line tangent to E(t) at t∗. Label the coordinates of the intersection (be careful that your scales for the two functions match).

In deciding how long a resident’s shift in the emergency room should be, the Chief of Staff at Vancouver General Hospital would like to minimize the average rate at which errors are made. Let E(t) be the number of errors made by a resident from the start of a shift until t hours into the shift. The instantaneous rate of change of errors made is E′(t) = t3 − 3 t2 + 2. Explain, as you would to a hospital administrator, why it makes sense to minimize A(t) rather than E(t).

In deciding how long a resident’s shift in the emergency room should be, the Chief of Staff at Vancouver General Hospital would like to minimize the average rate at which errors are made. Let E(t) be the number of errors made by a resident from the start of a shift until t hours into the shift. The instantaneous rate of change of errors made is E′(t) = t3 − 3 t2 + 2. What is the average rate of change of E(t) from the start of a shift (t = 0) up until time t? Call it A(t).

Find the derivative f 0 m(x) of the following function with respect to x:

fm(x) = (mΣ n=1 n^x · x^n )^2

Prove this identity between two infinite sums (with x ∈ R and n! stands for factorial):
(∞Σn=0x^n/n!)^2=∞Σn=0(2x)^n/n!

y=ײ-2×+5

if a function f is not defined at x=a that the limit