Calculus Answers

The region bounded by y=3-e^-x, the x-axis, x=2 and the y-axis.

How to complete rational numbers? Mention processes.

Solve for the confidence interval estimate of the population proportion.

Mikay conducted poll survey in which 520 of 1200 randomly selected voters indicated their preference for a certain candidate. What is the true population proportion of voters who prefer the candidate using 95% confidence interval?

The function,

f(x,y)= { x ; y is rational

{ 0 ; y is irrational

is integrable or not

True or false with full explanation

4.The profit function and the average cost function for a product of a company are

p(x) = - 4000 + 194x - 0.149x² in ringgit and ________ 4000

C(x) = 6 - 0.001x + ^________

^x

ringgit respectively, when x is the quantity sold in units. Find

(a) the total cost function

(b) the revenue function

(c) the quantity which will maximize the profit

(d) the maximum profit

(e) the price at maximum profit

1-Calculate the third-degree Taylor polynomial about x₀=0 for f (x) =(1+ x)^1/2

2-Use the polynomial in part (i) to approximate (1.1)^1/2 and find a bound for the

error involved.

3.Use the polynomial in part (i) to approximate integration[0,0.1]

(1 +x)^1/2dx .

∮[(z - 1)/(z(z - t)(z - 3i)) dz] ; |z - i| = 1/2

Determine the area of the region bounded by y = x² and y = 2x + 3

use the technique of derivative to find dy/dx

y=3 sin^5 x

y= sin t/ t

the task is to derive an equation for dy/dt using the quotient rule.