My name is Dakarai Holcomb, a student pursuing a degree in computer engineering at Georgia Southern University. I have been a tutor since spring semester 2021. I have loved helping any tutees that may need help in calculus 1 to 3 as well as physics 1 and 2. When they come in a few days after their quiz or test and tell me how well they did on it, I can't help but to have the biggest smile on my face.
Explain what it means to say that$ \displaystyle \lim_{x\to1^-}f(x) = 3 $ and $ \displaystyle \lim_{x\to1^+}f(x) = 7 $
In this situation is it possible that $ \displaystyle \lim_{x\to1}f(x) $ exists?Explain.
The acceleration function (in $ m/s^2 $) and the initial velocity are given for a particle moving along a line. Find (a) the velocity at time $ t $ and (b) the distance traveled during the given time interval.
$ a(t) = t + 4 $, $ v(0) = 5 $, $ 0 \le t \le 10 $
If $ a $ and $ b $ are positive numbers, show that$$ \int^1_0 x^a(1 - x)^b \,dx = \int^1_0 x^b(1 - x)^a \,dx $$
In the following exercises, solve and write your answer in mixed units. Leilani wants to make 8 placemats. For each placemat she needs 18 inches of fabric. How many yards of fabric will she need for the 8 placemats?
Among all of the pairs of numbers whose sum is 6, find the pair with the largest product. What is the product?
A rectangular storage container with an open top is to have a volume of $ 10 m^3 $. The length of its base is twice the width. Material for the base costs \$ 10 per square meter. Material for the sides costs \$ 6 per square meter. Find the costs of materials for the cheapest such container.
