Search & Filtering
(a) find and classify the critical points of the functions f(x) = 2x^3 + 3x^2 - 12 x +1 into maximum, minimum and inflection points as appreciate.
(b) The sum of two positive numbers is S. find the maximum value of their product.
1. Find the derivative of the following functions with respect to x.
(a) f(x) = x^-1/2 minus xe^x + 10^x + e^x^2 / 2x minus cube root of 15
(b) F(x) = e^x sinx + sec x + ln x^2
2. If y^5 + 4xy^3 + x^3 +1 =0, find dy / dx and determine its values at the point ( x, y) = ( 0, -1).
1. Evaluate the following limits
(a) Lim y"\\to" -1 Fourth root of 4y^3 minus 3
(b) lim x"\\to" infinity 1+x all over 1-x
(c) lim x "\\to" 2 x - 2 all over 4 - x^2
(d) lim x "\\to" 0 sinx - x cos x all over x^3
9.a) Check whether the series sum_(m=1)^(oo)(n^(2)x^(5))/(n^(4)+x^(3)) x in 0 alpha is uniformly convergent or not where alpha in R^(+).
show that∑n=0∞ (-1)^(n+1)(5)/(7n+2)` is conditionally convergent
[√n^4+9-√n^4-9]∞∑n=0 test the congervence
The population of a certain community is known to increase at a rate proportional to the number of people present any time.if the population had double in 5 years,how long will it take to triple?
1. Suppose a population of virus causing this pandemic known as COVID19
increases according to the law of exponential growth. Let’s say there were 130
viruses on the third day and 380 viruses on the seventh day. Approximately
how many COVID-19 viruses were in the original population?
2. How long will it take for an entrepreneur with an investment worth Php185,000
to double its worth if it is valued at Php260,000 two years after? What is the
exponential equation model for the investment?
3. A certain strain of virus being observed in a laboratory doubles its number
every 12 hours. The virologist counted the virus population to be 350. How
many viruses will there be in 10 hours?
4. The development of vaccines slows down the infection rate of a certain cow
disease exponentially. As of now, 900 cows are infected and in 2 days, only
556 cows are still expected to be infected. How many cows were initially
infected 5 days ago?
Solve the following real-life problems involving growth and decay.
1. There are 10.14 million people in Region III in 2010. It rose to11.22 million in
the year 2015, respectively. If it follows an exponential growth, what will be
our population in the year 2020?
2. After 15 years, what will be the mass of a 648-gram radioactive material
that has a half-life of 9 years?
3. Mr. Alfredo’s investment on a certain product is valued at P578,000
after 5 years and rose to Php 789,000 after 7 years. How much did he
invest initially?
4. (from question no. 3.) What will be the value of his investment after 10
years?
5. The population of pigs in a certain province is 6,500. But because of
African Swine flu, it went down to 4200 after 6 months. How many
months will it take to reduce the whole population to 400, if intervention
measures to save the pigs wer e not applied?
Draw the function f(x) = pi/L x defined in the interval -L < x < L and obtain its Fourier series expansion
