Math Answers

using ϵ−δ definition, show that

lim _x→2 (1/2 x² - x + 1)

Using the definition of limit at infinity or infinite limits, prove that

a) lim_{𝑥 → 3} 1/ (𝑥 − 3) ² = ∞ 

 Using Intermediate Value Theorem, show that

x2 = √𝑥 + 1 has a root in (1,2)

An element with mass 590 grams decays by 19.5% per minute. How much of the element is remaining after 15 minutes, to the nearest 10th of a gram?

A random sample of 900 members is found to have a mean of 4.45 CM can it be reasonably regarded as a sample from a large population whose mean is 5 cm and variance is 4 cm square obtain the 95% confidence limit for the mean in the population

A spider climbing out of a well is affected by the weather. When it rains, he falls back down the well with a probability of 1/10. In dry weather, he only falls back down with probability of 1/25. The probability of rain is 1/5.

(i) Draw the tree diagram of these events.

(ii) Find the probability he falls back down the well.

(iii) Find the probability that given he falls it was a rainy day.

Suppose that the sitting​ back-to-knee length for a group of adults has a normal distribution with a mean of 24.5in. and a standard deviation of 1.1in. These data are often used in the design of different​ seats, including aircraft​ seats, train​ seats, theater​ seats, and classroom seats. Instead of using 0.05 for identifying significant​ values, use the criteria that a value x is significantly high if​ P(x or ​greater)0.01 and a value is significantly low if​ P(x or ​less)0.01. Find the​ back-to-knee lengths separating significant values from those that are not significant. Using these​ criteria, is a​ back-to-knee length of 26.7in. significantly​ high?

Show that each of these conditional statements is a tautology

by using truth tables.

a) [¬p ∧ (p ∨ q)] → q

b) [(p → q) ∧ (q → r)] → (p → r)

c) [p ∧ (p → q)] → q

d) [(p ∨ q) ∧ (p → r) ∧ (q → r)] → r

Find the Derivative of the following function

1. y = x² cos x - 2xsinx - 2cosx
2. x(cos2x + 3y) = ysinx