Calculus Answers

An environmental study of a certain suburban community suggests that its average daily level of carbon monoxide will be 𝐶(𝑓) = √0.5𝑝 2 + 17 Parts per million when the population is p thousand. It is estimated that t years from now, the population of the community will be 𝑝(𝑡) = 3.1 + 0.1𝑡 2 thousand. At what rate will the carbon monoxide level be changing with respect to time 3 years from now?

Differentiate the function 𝑓(𝑥) = (3𝑥 + 1) 4 (2𝑥 − 1) 5 and simplify your answer

Find 𝑑𝑦 𝑑𝑥 if 𝑦 = 𝑢 3 − 3𝑢 2 + 1 and 𝑢 = 𝑥 2 + 2 

A manufacturer estimates that when q units of a certain commodity are produced, the total cost will be

C(x) rand where

C(q) = q2

25 + 80 000 − 104q.

Answer the following questions:

(i) Use marginal analysis to determine the production level at which the cost will be a minimum.

(ii) Determine the minimum cost.

Evaluate limits involving the expressions (sin t/t), (1 - cos t)/t) and ((e ^ t- 1)/t) and indeterminate forms type "0/0"

Directions: Create example of limits of functions and evaluate their limits.

1.(sint)/t

2.(1 - cos t)/t

3.(e ^ t - 1)/t

1.(sint)/t

2.(1 - cos t)/t

3.(e ^ t - 1)/t

Evalute limits involving the by constructjng their respective table of values

1.lim t -> 0 t/(sin t)

2.lim t -> 0 (sin t)/(2t)•(1 - cot t)/t

3.lim t -> 0 (e ^ t - 1/t)

A company determines that in order to sell x

x

 items the price per item, in dollars, must be p(x)=1830

p(x)=1830. The company also determines that the total cost, in dollars, to produce x x

 items is given by C(x)=3100+610x+1.5x2C(x)=3100+610x+1.5x2. 

How many items must the company produce and sell in order to maximize profit? 

The company must produce and sell 

A) If you get a slice of pizza with perimeter 90cm,what will be the diameter of the pizza for you to have gotten the largest pizza?

B)A curve passes through the point (0,5) and has the property that the slope of the curve at every point P is twice the y -coordinate of P. What is the equation of the curve?

Consider the curve y= f(x) for the function f(x)=e^2x-x^2

a)identify the domain of f

b)Find x,y-intercept

c)find the first and second derivatives

d)the critical points of the function f

e)where is the curve decreasing and increasing

F)find the point of inflection if any and discuss the concavity of the curve

G)Identify any asymptotes